i-NRLF 


HINRICHS:  The  Proximate  Constituents 

OF  THE 

Chemical  Elements. 


FOR  PLATE  6. 


I'.y   mistake,  the  cut    for  complex  instead  of    simplf  Terminal   Substitution, 
-I'i'ted  on  Plate  5.' 
very  similar  figure  here  printed  is  the  one  actually  referred  to  in  ; 


<9 


THE 

PROXIMATE   CONSTITUENTS 


OF  THE 


Chemical   Elements 


THE 

PROXIMATE  CONSTITUENTS 


OF  THE 


Chemical   Elements 

MECHANICALLY  DETERMINED  FROM  THEIR 

PHYSICAL  AND  CHEMICAL  PROPERTIES 


BY 

GUSTAVUS    DETLEF    HINR1CHS,    M.  D.,   LL.D., 

n 

Honorary  and  Corresponding  Member  of  Scientific  Societies  in 

Austria,  England,  France,  Germany  and  the  United  States ; 

Professor  of  Chemistry  in  the  Medical  Department, 

St.  Louis  University. 


WITH  32  PLATES. 


ST.  LOUIS,  MO.,  U.  S, 

CARL  GUSTAV  H1NRICHS,  PUBLISHER. 

New  York  and  Leipzig,   LEMCKE  AND  BUECHNER. 
London,  H.  GREVEL  &  CO.     Paris,  H.  LE  SOUDIER. 

1904. 


COPYRIGHT,  1904, 
GUSTAVUS  DETLEF  HINRICHS. 


STACK 

V 

GIFT 


Press  of  Nixon-Jones, 
216  Pine  Street,  St.  Louis. 


H53 


TO 
PROFESSOR,  DOCTOR 

CLEMENS  ALEXANDER  WINKLER, 

Geheimer  Rat, 
EhrenmitgHed  des  Professoren  Kollegiums 

der  Koniglich  Sachsischen 
BERGAKADEM1E  ZU  FREIBERG, 

HONOR-PRESIDENT 

of  the 

FIFTH  INTERNATIONAL  CONGRESS 
OF  APPLIED  CHEMISTRY, 


THIS  VOLUME 

IS  DEDICATED  BY 


THE  AUTHOR, 


PREFACE. 

When  a  boy,  I  often  wondered  at  the  meaning  of  the  following 
inscription*  on  a  large  stone  in  the  high  gable  of  one  of  the  grand 
old  houses  in  my  native  town : 

EL  HOMBRE  CUERDO  HA  DE   PEN 

SAR    QUE    MIENTRAS    VARIERA   EN 

ESTA    VI  DA    LA    FELICID^D    TIENE 

FOR    EMPRESTADA     Y     LA    ADVER 

SIDAD    POR    SU    NATURAL 

PATRIMONIO 

1649. 

When  a  young  man,  I  read  in  our  modern  histories  of  science 
of  the  manifold  persecutions  which,  in  darker  ages,  were  the 
reward  of  men,  who  had  dared  to  push  beyond  the  beaten  tracks 
of  the  schools  and  authorities  to  greater  heights,  and  thus  had 
cleared  away  errors  and  shown  Nature  in  a  brighter  light ;  and  I 
rejoiced  that  the  powers  of  darkness  and  superstition  happily  had 
been  dispelled  before  my  day  by  a  more  enlightened  civilization 
to  which  all  deeper  knowledge  would  be  welcome. 

After  half  a  century  of  incessant  labor  in  a  new  field  of  resea  rch 
full  of  intrinsic  difficulties,  I  have  found  the  boasted  modern 
civilization  only  more  refined  and  varied  in  its  methods  of  perse- 
cution and  of  torture.  Some  fine  instances  may  be  read  in  my 
Darkest  America;  see  also  footnote,  p.  xi  of  this  book. 

Therefore  much  time  and  labor  has  been  withdrawn  from  the 
loved  work  of  research,  and  I  have  not  yet  been  permitted  to 
complete  my  final  exposition  of  the  mechanics  of  the  three  states 
of  aggregation  and  the  structure  of  the  crystals. 

I  have  temporarily  left  this  main  work  in  order  to  present  by 
the  inductive  method  one  of  its  broadest  results  in  this  popular 


*  Evidently  the  experience  of  some  persecuted   Spaniard  who  had 
sought  a  place  of  refuge  among  the  Ditmarsians :  — 

"The  wise  man  must  remember  in  this  changeful  life:  happiness  is 
"but  a  loan,  and  adversity  his  natural  heritage." 

(vii) 


Vlll 

treatise  on  the  proximate  constitution  of  the  chemical  elements, 
at  the  time  of  the  International  Congress  of  Arts  and  Science, 
to  which  Ostwald,  Van't  Hoff  and  others  have  been  called  from 
across  the  sea,  to  instruct  us  in  the  Methodology  of  Science  and 
on  the  Constitution  of  Matter. 

If  mathematical  deduction  and  the  concordant  results  of 
physical  and  chemical  determinations  are  to  be  relied  on,  the 
published  teachings  of  some  of  these  prominent  scientists  are 
decidedly  in  error  and  positively  antiquated  on  points  of  funda- 
mental importance,  though  these  teachings  continue  to  be  accepted 
in  the  schools  because  the  authority  and  power  of  the  official 
station  of  these  men  represses  just  criticism,  as  Ostwald  himself 
has  delighted  to  explain  in  reference  to  a  preceding  generation. 

It  remains,  however,  to  be  seen,  whether  the  rising  generation 
will  ratify  the  punishment  for  such  criticism  of  human  authority 
by  the  suppression  of  my  name  while  quoting  and  using  my  re- 
sults admitted  to  be  "  admirable ;  "  possibly  it  may  happen,  that 
the  power  of  human  authority  will  fail  against  truth,  even  in 
Science. 

That  this  deplorable  and  reactionary  punishment  for  the  hold- 
ing scientific  truth  above  men  however  high  in  public  station,  is 
not  and  has  not  been  deemed  proper  by  all  prominent  modern 
men  of  science,  I  am  happy  to  demonstrate  by  the  portraits  and 
handwritings  of  some  of  the  eminent  scientists,  who  have  kindly 
encouraged  and  assisted  me  in  my  life  work. 

GUSTAVCS  DETLEF  HINRICHS. 
SAINT  Louis,  September  2,  1904. 


Publications  on  Atom-Mechanics. 

By  GUSTAVUS  D.  HINR1CHS,  1864-1904. 


A  list  of  my  books  and  publications  on  other  branches  has  not 
been  issued  since  1885.  They  treat  of  Mathematics,  Astronomy, 
Technical  Chemistry,  General  Laboratory  Teaching,  and  are  rela- 
tively extended  on  Meteorology,  including  Meteorites. 


I.     Books* — Entirely  or  largely  devoted  to  this  subject. 

Programme  der  Atom-Mechanik,  die  Chemie  eine  Mechanik  der  Pan- 
Atome. — 44  pp.  4  vo.,  Iowa  City,  1867.  French  Resume  of  same, 
4  pp.  4vo.,  November,  1867.  English  Resume,  4  pp.  4vo.; 
August,  1867. 

The  Principles  of  Pure  Crystallography. — Pp.  IV,  44,  in  8vo.;  Dav- 
enport and  Leipzig,  1871.  See  especially,  Chapter  VI. 

The  Method  of  Quantitative  Induction  in  Physical  Science. — Dav- 
enport and  Leipzig,  1872.  See  especially  the  last  section,  p.  36, 
giving  the  Mechanics  of  the  three  States  of  Aggregation. 

The  Principles  of  Chemistry  and  Molecular  Mechanics. — 200  pp., 
8  vo.,  with  two  plates.  Cloth.  Davenport  and  New  York,  1874. 
Especially  pp.  63-66;  110-137;  151-152;  165-182. 

Beitrage  zur  Dynamik  des  Chemischen  Molekuels.  Leipzig,  Gustav 
Fock,  1892:  I.— The  Molecule  as  a  System  of  Material  Points. 
II. — The  Energy  of  the  Molecule.  III. — Graphical  Structural 
Formula.  IV. — The  Moments  of  Inertia  of  the  Molecules.  V. — 
The  Motions  of  the  Molecules.  VI. — The  Boiling  Points  of 
Isomeric  Bodies  Determined  by  the  Moment  of  Inertia  of  the 
Molecules.  These  papers  were  first  sent  to  the  Deutsche 
Chemische  Gesellschaft,  I,  II,  April,  1872;  III- VI,  April,  1873,  of 
which  I  was  a  member.** 

The    True    Atomic    Weights    of    the    Chemical    Elements,    and    the 


*  The  catch-word  specially  accentuated  will  be  used  for  brief  ref- 
erences in  quotations. 

**  The  most  remarkable  history  of  the  original  paper  is  given  in 
the  edition  of  1892. 


(ix) 


Unity  of  Matter.— Pp.  XVI,  256,  8  vo.,  7  plates,  many  illustra- 
tions; fine  paper,  cloth  binding.    St.  Louis  and  New  York,  1894. 

Introduction  to  General  Chemistry. — A  graded  course  of  100  lec- 
tures, with  an  Atlas  of  80  plates,  representing  Chemists,  Insti- 
tutions, Prime  Materials,  Crystals,  Diagrams  and  Apparatus; 
400  pages,  8vo.;  bound  in  cloth.  St.  Louis  and  New  York,  1897. 
Especially  lectures  91  to  100  (pp.  350-382). 

The  Absolute  Atomic  Weights  of  the  Chemical  Elements  *  *  * 
and  the  Unity  of  Matter. — With  portrait  of  Berzelius  anl  three 
plates.  St.  Louis,  1901;  XVI,  304  pp.  $8.00. 

Introduction  to  Crystal lographic  Chemistry — 36  pp.  text  and  40  pp. 
plates.  8  vo.  Issued  as  introduction  to  first  course  in  Micro- 
chemical  Analysis  by  Carl  Gustav  Hinrichs.  St.  Louis,  New 
York  and  Leipzig,  1904.  156  pp.,  8  vo.,  of  which  64  pp.  plates. 

The  Proximate  Constituents  of  the  Chemical  Elements  mechanically 
determined  from  their  Physical  and  Chemical  Properties.  St. 
Louis,  New  York  and  Leipzig,  1904.  8  vo.  32  pp.  plates,  112 
pp.  text. 

II.  Academy  of  Sciences  of  Vienna. — Stizungsberichte.     Presented 
by  Wilhelm  Haidinger.    On  the  (Crystal)  Structure  of  Quartz.— 
I  Abthl.,  vol.  61,  pp.  83-88,  1870.    On  the  Statics  of  Crystal-Sym- 
metry.— II  Abthl.,  vol.  62,  pp.  345-361,  1870.     Chemico-Physical 
remarks  on  the  Reality  of  Rhombo-Tesseral  Forms. — Anzeiger, 
1869,  No.   1. 

III.  Academy  of  Sciences  of  Paris. — Comptes  Rendus.     Presented 
by  Marcelin    Berthelot.     For  reference*,  these  papers  will  be 
specified  by  number  as  "Notes." 

FIRST    SERIES. — General    Mechanics    of   the    Three    States    of 
Aggregation. 

I. — On  the  Molecular  Rotation  of  Gases.    June  2, 1873. — T.  76,  p.  1357. 

II. — On  the  Boiling  Points  and  the  Molecular  Volumes  of  the  Iso- 
meric  Chlorides  of  the  Ethyl  Series.  June  9,  1873.— T.  76,  p  1408. 

III. — On  the  Calculation  of  the  Moments  of  Inertia,  of  Molecules. 
June  30,  1873.— T.  76,  p.  1592. 

IV. — On  the  Atomic  Structure  of  the  Molecules  of  Benzine  and 
Terebene.  January  4,  1875. — T.  80,  p.  47. 

V. — Calculation  of  the  Maximal  Moments  of  Inertia  of  the  Mole- 
cules of  the  Chlorine  Derivatives  of  Toluene.  March  1,  1875. — 
T.  80,  p.  565. 

VI. — On  the  Determination  of  the  Boiling  Points  of  the  Chlorine 
Derivatives  of  Toluene.  March  22,  1875. — T.  80,  p.  766. 


*  The  date   of   the   session   and   volume    (T,    tome,    and   page   are 
given. 


SECOND    SERIES.* — The  General  Relations  Between  Boiling  Point, 
Pressure  and  Atomic  Weight  and  Form  of  Compounds. 

VII. — Statement  of  the  General  Law  determining  the  Fusing  and 
Boiling  Points  of  any  Compound  under  any  Pressure,  as  Simple 
Function  of  the  Chemical  Constitution  of  the  same.  May  4, 
1891.— T.  112,  p.  998. 


*  As  resident  member  of  a  certain  Academy  of  Science  I  read  at 
its  meetings,  in  the  Fall  of  1890  and  Winter  of  1891.  several  papers, 
covering-  the  ground  of  this  second  series,  which  papers  are  men- 
tioned by  title  in  the  published  proceedings  of  that  Academy. 

No  steps  to  their  publication  being  taken,  I  stopped  my  scientific 
contributions  to  this  Academy  and,  in  order  to  protect  my  scientific 
work,  sent  on  April  17,  1891  a  note  (No.  VII  of  this  list)  to  M.  Berthe- 
lot  of  the  Academy  of  Science  of  Paris. 

Already  on  May  1,  1891,  I  received  the  following  cablegram  from 
Paris,  of  same  date  which  also  is  the  date  on  which  Bertlielot  re- 
ceived my  letter  and  manuscript: 

"Your  note   will  be  printed   in   the  Comptes   Rendus   before 
"the    15th    of   May.      Berthelot." 

My  note  was  presented  to  the  French  Academy  by  M.  Berthelot 
at  its  first  meeting  after  the  receipt  of  my  paper,  namely  on  May  4th, 
1891. 

The  number  of  the  Comptes  Rendus  of  that  meeting,  containing 
my  paper,  was  issued  according  to  rule  on  the  day  of  the  next  meet- 
ing, which  was  on  May  11.  Thus  the  promise  given  by  the  cable- 
gram was  fulfilled  to  the  letter. 

This  simple  statement  of  facts  and  dates  I  will,  at  this  time,  sup- 
plement with  only  the  further  statement,  that  some  defect  in  my 
English  was  intimated  to  have  been  detected  by  some  eminent  scholar 
on  the  committee  on  publication  of  our  local  Academy  of  Sciences. 

I  therefore  sent  a  paper  of  mine  to  the  London  "Nature".  In  the 
number  of  this  first  class  English  journal  of  June  25,  1891  I  found, 
that  paper  printed  exactly  as  written  by  me;  I  have  kept  the  dupli- 
cate carbon  thereof. 

Since  now  my  Science  was  accepted  promptly  and  published  im- 
mediately by  the  Academy  of  Science  of  Paris,  and  since  my  English 
was  good  enough  for  one  of  the  best  of  the  scientific  journals  of  Lon- 
don, I  tried  to  forget  the  treatment  received  from  the  few  fellow- 
members  of  our  local  Academy  of  Science,  who  mismanaged  its  af- 
fairs. 

With  some  difficulty  I  re-obtained  possession  of  my  original  pa- 
pers, which  I  have  carefully  preserved  in  my  safe  on  account  of  the 
few,  but  no  doubt  highly  inportant  and  most  valuable  improvements 
in  science  and  languague  marked  by  the  eminent  censors,  but  which 
improvements  I  have  not  yet  had  occasion  to  publish  for  the  benefit 
of  the  scientific  world. 

Regretting  that  the  traits  so  prominent  in  some  of  our  political 
meetings  are  not  strangers  in  professedly  scientific  societies,  I  have 
tried  to  get  along  in  my  scientific  work  without  again  seeking  any 
of  the  advantages  for  which  that  Academy  of  Sciences  was  founded. 

Possibly  such  management  may  largely  account  for  the  rather 
insignificant  work  our  Academies  of  Sciences  accomplish  in  the  ad- 
vancement of  science. 


Xll 

VIII.— Calculation    of   the    Fusing   and    Boiling    Points   of   Normal 

Paraffins.     May  19,  1891.— T.  112,  p.  1127. 
IX. — Calculation  of  the   Boiling  Point  of  Any  Liquid   Under  Any 

Pressure.     June  22,  1891. — T.  112,  p.  1436. 
X. — Calculation   of  the  Molecular  Volume.     July   6,  1891.— T.   113, 

p.   36. 
XI. — Mechanical  Determination  of  the  Linkage  of  the  Carbon  Atoms 

in  Organic  Compounds.     August  17,  1891. — T.  113,  p.  313. 
XII.— Calculation  of  the  Specific  Heat.     October  12,  1891.— T.  113, 

p.  468. 

XIII. — Calculation  of  the  Magnetic  Rotation  of  the  Plane  of  Polar- 
ization of  Light.     October  19,  1891. — T.  113,  p.  500. 
XIV.— Mechanical  Determination  of  the  Position  of  the  Hydrogen 

Atoms   in   Organic   Compounds.     November  23,   1891.— T.    113, 

p.  743. 
XV. — Calculation  of  the  Boiling  Point  of  the   Isomeric  Ethers   of 

the  Fatty  Acids.     December  7,  1891.— T.  113,  p.  798. 

THIRD    SERIES.— The    General    Mechanical    Effects    of    Chemical 

Substitution. 

XVI. — Calculation  of  the  Boiling  Point  of  Compounds  Derived  From 
the  Paraffins  by  Terminal  Substitution.  March  14,  1892. — T. 
114,  p.  597. 

XVII. — Determination  of  the  Boiling  Surface  of  the  Normal  Paraffins. 
May  2,  1892.— T.  114,  p.  1015. 

XVIII. — Establishment  of  the  Formulae  for  the  Calculation  of  the 
Maximal  Moments  of  Inertia.  May  9,  1892. — T.  114,  p.  1064. 

XIX. — Mechanical  Determination  of  the  Boiling  Points  pf  Com- 
pounds of  Simple  Terminal  Substitution.  May  16.  1892. — T. 
114,  p.  1113. 

XX. — Mechanical  Determination  of  the  Boiling  Points  of  Com- 
pounds of  Complex  Terminal  Substitution.  May  30,  1892.— T. 
114,  p.  1272. 

XXI. — Mechanical  Determination  of  the  Boiling  Points  of  Alcohols 
and  Acids.  June  7,  1892.— T.  114,  p.  1367. 

XXII. — On  the  Mechanical  Contrast  Between  the  Radical  Cyanogene 
and  the  Chloroid  Elements.  July  18,  1892.— T.  115,  p.  177. 

XXIII. — The  Specific  Heat  of  the  Atoms  and  Their  Mechanical  Con- 
stitution. July  25,  1892.— T.  115,  p.  239.. 

XXIV. — On  the  General  Form  of  the  Boiling  Point  Curves  ofi  the 
Compounds  Resulting  from  Central  Substitution.  August  8, 
1892.— T.  115,  p.  314. 

FOURTH     SERIES.— Determination    of    the    True    Atomic    Weight 
of   the    Elements. 

XXV. — Critical  Reduction  of  Fundamental  Determinations  of  Stas 
on  Potassium  Chlorate.  December  12,  1892. — T.  115,  p.  1074. 


Xlll 

XXVI. — On  the  Determination  of  the  Atomic  Weight  of  Lead  by 

Stas.     February  27,  1893. — T.  116,  p.  431. 
XXVII. — General  Method  for  the  Calculation  of  the  Atomic  Weights 

From   the   Results   of  Chemical   Analysis.     March   27,   1893. — 

T.   116,  p.   695. 
XXVIII. — Determination  of  the  Atomic  Weight  by  the  Limit  Method. 

April  10,  1893. — T.  116,  p.  753. 
XXIX. — Determination   of  the   True  Atomic  Weight  of  Hydrogen. 

November   13,   1893.— T.   117,  p.  663. 
XXX. — Outline   of   the    System   of   Atomic   Weights   of   Precision, 

Based  Upon  the  Diamond  as  Standard  of  Matter.     December 

26,   1893.— T.   117,   p.   1075. 
XXXI.— On  the  Atomic  Weights  of  Precision,  Determined  by  Using 

Silver   as    Secondary   Standard   of   Matter.     March   5,   1894. — 

T.  118,  p.   528. 
XXXII. — On  the  Atomic  Weight  of  Boron.     June  18,  1900. — T.  130, 

p.   1712. 
XXXIII.— On    the    Atomic    Weight   of   Ten   Elements    Determined 

From  Recent  Experiments.     July  2,  1900. — T.  131,  p.  34. 

FIFTH    SERIES.— Diverse   Topics. 

XXXIV. — On  the  Composition  of  the  Air  in  the  Vertical,  and  on 
the  Constitution  of  the  Higher  Strata  of  the  Earth's  Atmos- 
phere. August  20,  1900.— T.  131,  p.  442. 

XXXV. — Preliminary  Notice  of  an  Inverse  Genus  of  Common  Me- 
teoric Stones.  Presented  by  A.  Daubree.  June  18,  1894. — T. 
188,  p.  1418. 

XXXVI. — The  Oscillation  of  Mid-November  in  America.  Presented 
by  Chas.  St.  Claire-Deville.  February  28,  1876. — T.  82,  p.  520. 

IV.  Contributions  to  Molecular  Science — Being  Reprints  from  the 
Proceedings  of  the  American  Association  for  the  Advancement 
of  Science. 

Chicago   Meeting,   1868 

1.  The   Statics   of   the   Four   Types   of   Modern   Chemistry,   With 
Especial  Regard  to  the  Water  Type.    Vol.  17,  pp.  207-223. 

2.  A  New  and  General  Law  Determining  the  Atomic  Volume  and 

Boiling  Point  of  a  Great  Number  of  Carbon  Compounds.    Vol. 

17,  pp.  223-238.     1868. 

On  the  Calculation  of  the  Crystalline  Form  of  the  Anhydrous 
Carbonates,  Nitrates,  Perchlorates,  Permanganates,  and 
Other  Salts  of  Like  Composition.  Vol.  17,  p.  345.  1868. 
Read  by  title. 

Salem    Meeting,   1869: 

3.  On  Molecular  Perturbations.     Vol.  18,  pp.  100-112.     1869. 

4.  On  the  Classification  and  the  Atomic  Weights  of  the  So-Called 


XIV 

Chemical  Elements,   With  Reference  to  Stas'   Determinations. 

Vol.   18,   pp.    112-124.      1869. 

On  Atomic  Volume  and  Atomic  Distances  of  the  Crystallized 

A  B3  C.     Vol.  18,  p.  275.     1869.     Read  by  title. 
The  following  papers  were  read,  but  not  printed,  the  Associa- 
tion now  publishing'  its  proceedings  late  and  with  abstracts  only: 

Dubuque    Meeting,    1872: 

On  the  Dynamical  Conditions  of  the  Three  States  of  Aggregation. 
Vol.  21,  p.  258.  1872. 

Washington    Meeting,   1891: 

Statement  of  the  General  Law  Determining  the. Fusing  and  Boil- 
ing Point  of  Any  Compound,  Under  Any  Pressure  as  Simple 
Function  of  the  Chemical  Constitution  of  the  Same.  Vol.  40, 
p.  144. 

The  Calculation  of  the  Boiling  Point  of  a  Liquid  Under  Any  Pres- 
sure. Vol.  40,  p.  141. 

Determination  of  the  Discontinuity  of  the  Fusing  Points  of  Paraffins 
by  Means  of  Analytical  Mechanics.  Vol.  40,  p.  141. 

The  Calculation  of  the  Boiling  Point  of  Any  Paraffin  Under  Any 
Pressure.  Vol.  40,  p.  190. 

The  Calculation  of  the  Boiling  Points  of  Isomerics  From  Their 
Moments  of  Inertia.  Vol.  40,  p.  190. 

Determination  of  the  True  Position  of  Carbon  Atoms  in  Organic 
Compounds  by  Means  of  Analytical  Mechanics.  Vol.  40,  p.  190. 

Rochester    Meeting,    1892: 

On  the  Mechanics  of  the  Three  States  of  Aggregation.    Vol.  41,  p.  90. 
On  the  Mechanical  Determination  of  the  Stereographic  Constitution 
of  Organic  Compounds.     Vol.  41,  p.  114. 

Madison    Meeting,   1893: 

On  the  Systematic  Errors  Affecting  All  the  Atomic  Weights  of 
Stas'.  Vol.  42,  p.  107. 

V.     Publications    in    Divers    Periodicals. 

American  Pharmaceutical  Association. — Forty-first  Annual  Meeting, 
Chicago,   August   14-20,   1893: 

On  the  Atomic  Weights  of  the  Chemical  Elements.     Minutes 
of  Proceedings,   Philadelphia,  1893;    pp.   104-106. 
American  Journal  of  Science: 

On  the  Distribution  of  the  Dark  Lines  in  the  Spectra  of  the 
Elements.     Vol.   38,  pp.   31-40.     1864. 

On  the  Spectra  and  Composition  of  the  Chemical  Elements. 
Vol.   42,   pp.    350-360.     1866. 


XV 

The  Crystalline  Form  of  the  Anhydrous  Carbonates.* 
American  Journal  of  Mining.     New  York,  1867: 

Synopsis  of  the  Programme  of  Atom-Mechanics.     June,  1867. 
Atom-Mechanics  Proved  by  Tyndall's  Experiments.     May  2, 
1868. 
Scientific  American.     New  York: 

How  a  Snowflake  Is  Built.     April  18,  1868.     Illustrated. 
The   Pharmacist.     Chicago: 

Natural  Classification  of  the  Elements.     July,  1869. 
Comptes  Rendus.     Academy  of  Science  of  Paris: 

Note  on  the  Crystal-Form  of  Sulphates.    T.  68,  p.  344.    1869. 
Zeitschrift  fur   Physikalische   Chemie.     Leipzig: 

On  the  Tension  of  Saturated  Vapor  of  Water.  Bd.  VIII,  p. 
680.  1891.  Also  in  Vol.  VIII  (1891),  the  following  of  the 
Second  Series  of  my  Contributions  to  Atom-Mechanics:  VII, 
p.  229;  VIII,  p.  232;  IX,  p.  340;  XI,  p.  677.  Also  in  Vol.  IX 
(1892) :  Contribution  X,  p.  81. 
Kruess  Zeitschrift  fuer  Anorganische  Chemie.  Hamburg: 

The   Determination   of  the   True  Atomic  Weight  of  Copper. 
Bd.  V,  p.   293.     1893. 
Chemical   News.     London: 

The  Specific  Heat  of  the  Atoms  and  Their  Mechanical  Con- 
stitution. Vol.  66,  p.  116.  Sept.  2,  1892. 

Determination  of  the  True  Atomic  Weight  of  Copper.     Vol. 
68,  p.   171.     Oct.  6,   1893. 
Nature.     London: 

Statement;  of  the  General  Law  Determining  the  Fusing  and 
Boiling  Points  of  Any  Compound  Under  Any  Pressure,  as  Sim- 
ple Function  of  the  Chemical  Constitution  of  the  Same.  June 
25,  1891. 


*  The  general  results  of  this  paper  were  published  in  the  July 
and  September  numbers  of  1867,  after  having  been  in  the  hands  of 
the  editor  during  the  months  of  March,  April  and  May,  1867.  Natur- 
ally, I  have  not  given  the  editor  a  chance  for  further  exhibitions  of 
what  he  calls  "independent  action  in  independent  minds." 


EMINENT   SCIENTISTS 


WHO  HAVE 

ENCOURAGED  AND  ASSISTED  THE  AUTHOR 
IN  HIS  WORK  ON 


ATOM-MECHANICS 


AND  THE 


COMPOSITION    OF   THE   CHEMICAL 
ELEMENTS 


FROM 


1855  to  1904, 


JOHANN  GEORG  FORCHHAMMER. 


Born  July  26,  1794,  at  Husum,  Slesvig;  died  December  14, 1865,  at  Copenhagen, 
Denmark.  Professor  of  Mineralogy  at  the  University  since  18H5  and  Professor  of 
Chemistry  at  the  Polytechnic  School,  both  of  Copenhagen;  Director  of  the  latter  since 
1851.  For  many  years'  the  most  noted  chemist  and  most  influential  man  of  science 
in  Denmark. 

I  have  been  under  great  obligations  to  Forchhammer  from  my  entrance  in  1853 
(see  Absol.  At.  Wghts.,  p.  84-5,  also  True  At.  Wghts.,  p.  51-55) .  Dedicated  my  first  book 
(Hamburg,  1856)  to  him.  Received  two  stipends,  one  of  100,  a  second  of  '200  Dalers  from 
the  Holstein  Government,  mainly  through  his  influence. 

The  above  autograph  are  the  closing  words  of  his  last  letter  to  me,  written  (Oc- 
tober 11,  1865)  only  two  months  before  his  death.  His  handwriting  (German)  always 
was  like  an  engraving  and  hardly  requires  a  translation;  he  "especially  wishes  me  the 
happiest  success  in  my  new  sphere  of  action  "  at  the  State  University  of  Iowa. 


FORCHHAMMER. 


WILHELM    HAIDINGER. 


Born  February  5, 1795,  at  Vienna,  Austria,  where  he  died  March  19,1871.  Haid- 
inger  was  one  of  the  most  noted  Mineralogists  and  Crystallographers  of  his  time,  one 
of  the  founders  of  the  Academy  of  Sciences  of  Vienna  (1847)  and  founder  of  the 
Geologische  Reichsanstalt  of  Austria,  also  greatly  developed  the  collection  of  Meteor- 
ites at  Vienna. 

The  first  letter  from  his  hand  is  dated  December  10, 1856;  the  last  bears  date  of 
December  2, 1870,' written  only  three  months  before  his  death.  My  biographical  sketch 
of  his  life,  with  a  fitte  lithograph  of  his  last  photograph,  was  published  in  1671  (IHpp. 
8vo.). 

I  am  not  oftly  indebted  to  him  for  many  encouraging  letters,  but  also  for  the 
presentation  of  two  of  my  crystallographic  papers  to  the  Academy,  published  in  the 
Sitzungsberichte  for  1870.  His  Mineralogie~(1845)  is  especially  profound  in  its  crystal- 
lographic part,  on  which  I  have  drawn  in  my  recent  Crystallographic  Chemistry 
(p.  10-11). 


HAIDINGER. 


FATHER  ANGELO  SECCHI,  S.  J. 


Born  June  29,  1818,  at  Reggio,  Emilia,  Northern  Italy;  died  February  2(5,  l*7v  .-it 
Rome.  Part  of  his  high  mathematical  training  he  received  at  the  University  of  his 
order  at  Georgetown,  near  Washington,  D.  C.,  where  he  also  spent  the  "  years  of 
exile,"  1848-9.  He  built  in  1852  and  directed  till  his  death  the  Astronomical  Observa- 
tory of  the  Collegio  Romano. 

He  is  famous  both  as  Meteorologist  (his  Meteorograph  was  shown  at  the  Paris 
Exposition  of  1867  and  won  the  prize  of  100,000  francs)  and  as  Astronomer,  being  the 
first  to  classify  the  stars  according  to  their  spectra  or  chemical  constitution.  His  most 
noted  works  are  "  The  Unity  of  the  Physical  Forces,"  1864,  and  "  The  Sun,"  the  second 
edition  forming  two  magnificently  illustrated  volumes  (1875  and  1877).  Quotations 
from  my  works  in  theirs*,  p.  495,  in  the  second,  Vol.  II,  pp.  377-381. 

His  letter  quoted  from  above  is  dated  "  Rome,  April  19,  1877,"  or  less  than  a  year 
before  his  death.  The  quotation  reads  in  English:  "In  this  work  and  in  several 
"  places,  I  have  been  encouraged  by  your  important  discoveries,  and  I  have  been 
"  greatly  profited  thereby." 


P.  SECCHI. 


^'/ 


MARCELIN  PIERRE  EUGENE  BERTHELOT. 


Born  October  25, 1827,  at  Paris.  For  half  a  century  a  most  successful  investigator 
and  writer,  especially  on  chemical  synthesis,  thermochemistry  and  the  history  <»t 
chemistry.  Since  1864  Professor  at  the  College  de  France,  and  since  1889  one  of  the 
two  perpetual  Secretaries  of  the  Academy  of  Sciences  of  Paris. 

Without  any  introduction  but  my  own  letter  he  presented,  in  June,  1873,  my  lirst 
Note  on  the  Rotation  of  the  Molecules.  He  has  since  presented  about  35  additional 
Notes  from  me  which  have  appeared  in  the  Comptes  Rendus  and  form  a  volume  of 
140  pages  in  quarto.  In  July,  1873, 1  had  the  honor,  as  his  guest,  to  explain  my  mathe- 
matical work  to  his  friend  Bertrand,  the  mathematician.  .The  t\vo  future  perpetual 
Secretaries  of  the  Academy  of  Sciences  of  Paris  were  the  most  interested  and  influ- 
ential students  ever  addressed  by  me.  My  "  True  Atomic  Weights  "  was  dedicated  to 
Berthelot.  I  most  sincerely  thank  him  and  the  French  scientists  for  the  courtesies 
extended  to  me  and  my  work. 

The  above  autograph  forms  the  closing  words  of  his  letter  of  May  4,  1897,  and 
reads  in  English :  *  *  *  and  I  hope  that  we  may  continue  for  still  a  long  time  both 
the  one  and  the  other  to  concur  in  the  progress  of  science.  Please  accept  the  assur- 
ance of  my  sentiments  of  high  esteem  and  affection. 


BERTHELOT. 


CHARLES  FRIEDEL. 


Born  March  12,  1832,  at  Stra?sburg,  Alsace  (then  France)  ;  died  April  20,  Ih'ju.  at 
Montuuban,  France.  Was  Professor  of  Mineralogy  at  the  School  of  Mines,  ami  of 
Organic  Chemistry  at  the  University  of  Paris. 

The  province  of  Alsace  was  torn  by  France  from  the  old  German  Empire  during 
the  dreadful  thirty  years'  war;  it  has  given  to  France  a  remarkably  large  number  of 
famous  men  who,  while  all  patriotic  Frenchmen,  in  their  life  work  revealed  their 
Teutonic  traits  as  plainly  as  in  their  name.  "The  pleiade  of  chemists  of  Alsare." 
composed  of  Gerhardt,  Wurtz,  Friedel  and  Schiit/enberger,  is  a  striking  example. 
Gerhardt's  revolutionary  work  aided  me  at  the  beginning  of  my  research,  the  others 
I  met  at  Paris,  in  1873.  The  last  two  have  since  greatly  helped  and  befriended  me. 
Friedel  honored  me  by  accepting  the  dedication  of  my  General  Chemistry  in  1S97. 

The  autograph  presented  is  the  close  of  his  letter  of  September  23, 1896:  "  I  i>«-^ 
"  you  to  accept.  Monsieur  and  dear  Colleague,  the  expression  of  my  cordial  devotion 
"  and  my  best  wishes  for  your  health." 


iff^ 


ml. 


FRIEDEL. 


PAUL  SCHUTZENBERGER. 

Born  December  '23,  1829,  at  Strassburg,  Alsace  (then  France),  died  June  26, 1897, 
at  Mezy,  France.  Professor  of  Chemistry  at  the  College  de  France  since  1876. 

This  renowned  chemist  of  "the  Alsace  Pleiade  "  carried  out  most  important 
researches  on  the  metals  of  the  rare  earths  in  the  hope  of  finding  some  proof  of  their 
complex  nature. 

In  a  public  lecture  at  the  Sorbonne  (the  University  of  Paris)  and  under  the  pre- 
sidence  of  Friedel,  Professor  Schiitzenberger  gave  to  an  audience  of  French  Chemists 
a  full  exposition  of  my  work  as  published  in  my  "  True  Atomic  Weights."  This  lec- 
ture forms  the  opening  article  of  the  new  chemical  journal  of  Friedel,  "  the  Actualites 
Chimiques,"  begun  1896.  Also  in  his  Revue  this  work  of  mine  is  placed  at  the  head. 
In  his  posthumous  "  Chimie  generale,"  Paris,  1898,  he  again  presents  the  same 
(pp.  143-152). 

The  autograph  of  November  10,  1894,  reads:  "  Highly  honored  Colleague.  I 
"  thank  you  very  much  for  your  line  work  which  you  have  sent  me  and  which  I  am 
"  now  reading  with  the  greatest  interest." 


SCHUTZENBERGER. 


CLEMENS  ALEXANDER  WINKLER. 


Born  December  26, 1838,  at  Freiberg,  Saxony,  Germany.  Since  1^7.".  I'mh-^or  oi 
Chemistry  in  the  Bergakademie  at  Freiberg,  the  oldest  technical  High  School  in  the 
world.  Some  of  the  most  noted  pioneers  in  special  branches  of  modern  scit -nc. •-  \\ n  < 
professors  of  this  famous  school. 

The  perfection  of  the  analytical  work  of  Winkler  astonished  me  till  I  found  tin- 
name  of  his  father,  Kurt  Winkler,  in  the  list  of  special  students  of  Berzelius.  The 
Academy  of  Sciences  of  Stockholm  has  published  some  of  Winkler's  investigations. 

Technical  gas  analysis,  the  manufacture  of  sulphuric  acid  by  the  contact  method, 
and  the  discovery  of  the  rare  element  Germanium,  have  long  ago  made  Winkler  known 
throughout  the  chemical  world. 

The  aBove  autograph  forms  the  conclusion  of  his  letter  of  October  6,  1901,  and 
reads  in  English:  "It  has  been  an  extended,  extremely  painstaking  labor  which  you 
"  in  this  book  have  presented  to  the.scientillc  world,  and  it  will  yield  you  the  richest 
"  recognition." 


WINKLER. 


CURRICULUM  VIT/E. 

GUSTAVUS  DETLEF  HINRICHS  was  born  Decembers,  1836, at  Lund,  ,,, 
in  North-Ditraarsia,  in  the  duchy  of  Holstein,  (then)  Denmark,  German  Confederation; 
now  province  of  Schleswig-Holstein,  Prussia,  Germany. 

Ditmarsia  was  for  many  centuries  an  independent  republic;  its  history  is  an 
account  of  heroic  resistance  to  more  powerful  neighbors.  The  combined  forces  of 
Holstein,  Schleswig  and  Denmark  finally  overcame  the  republic  in  1559.  Lunden  \va- 
the  chief  town  of  the  Northern  Half  of  the  Republic;  it  still  contains  buildings  and 
monuments  of  that  time. 

Father  was  surveyor  and  engineer;  several  ot  his  ancestors  were  prominent  in 
the  government  of  the  republic  as  far  back  as  1434.    Our  family  belonged  to  the  Vo^lr 
mannen,  originally  Vodiems,  coming  from  Frisia  about  1200  on  account  of  great  storm 
floods. 

Mother's  family  was  Danish;  ray  first  great  bereavement  was  the  death  of  my 
grandmother,  who  gave  me  my  first  instruction  in  Danish  stories. 

For  study  I  had  few  books,  but  made  the  most  of  them  — and  copied  from  such  I 
could  get  for  temporary  use.  I  have  still  quite  a  notebook  full  of  astronomical  excerpts 
written  when  I  was  ten  years  old.  Also  used,  at  that  time,  a  MS.  "  Steuermannskiindi-  " 
showing  how  the  ship's  place  at  sea  is  determined. 

The  general  revolution  of  1848  made  boys  old;  in  1850  I  ran  away  and  was  one 
day  at  the  fire  line.  Our  German  brothers  had  urged  us  on  in  1848.  In  184H  I'ru-^ia 
dropped  our  cause,  and  in  1852  the  German  I'owers  disarmed  us  and  turned  us  o\n 
again  to  Denmark.  This  abandonment  made  a  lasting  impression  on  me,  so  that  I 
agreed  with  family  and  assisting  friends  and  went  North  to  Copenhagen  to  study,  1853. 
The  mental  atmosphere  at  the  school  was  excellent.  Berzelius  and  Oersted  had 
departed  only  five  and  two  years  before. 

During  three  years  I  followed  the  regular  course  of  study,  for  five  years  there- 
after I  studied  what  I  seemed  to  require  for  my  scientific  life  work.  To  be  qualified 
to  teach  in  higher  scientific  schools  I  passed  the  examinations  early  in  I860,  mark 
"excellent." 

By  this  time  the  old  national  antagonism  broke  out  anew.  Many  friends  in  high 
position  in  Denmark,  nearest  relatives  in  the  Holstein.  I  had  to  go  into  a  foreign  land 
once  more,  and  arrived  in  America  on  the  eve  of  the  battle  of  Bull's  Run,  which  opened 
our  Civil  War  of  four  years'  duration. 

Became  teacher  in  a  district  school;  then  in  a  city  high  school,  next  in  the  pre- 
paratory school  of  a  State  University.  In  another  year  I  was  elected  Professor  in  that 
institution  which  I  served  for  a  quarter  of  a  century.  In  1889  I  was  called  to  the  city 
of  St.  Louis. 


I.  THE  CHEMICAL  ELEMENTS. 

GRAPHIC    REPRESENTATION    OF    THEIR  CHARACTERISTIC   PROPERTIES, 
AND    THEIR    DIVISION    INTO    FAMILIES    OR    GENERA. 

The  world  of  matter  presents  to  us  a  most  astounding  variety 
of  substances  ;  they  differ  in  every  conceivable  way.  When  by 
our  senses  unaided  we  suppose  we  have  found  two  substances 
apparently  identical,  we  very  often  find  great  differences  in  prop- 
erties as  soon  as  we  call  to  the  assistance  of  our  senses  some  of 
those  manifold  instrumental  aids  that  modern  science  has  provided. 

If  we,  by  any  and  all  means  now  at  our  disposal,  begin  the 
work  of  chemical  decomposition  of  any  of  the  natural  bodies, 
whether  animal,  vegetable  or  mineral,  we  obtain  gradually  more 
and  m  .re  simple  products  ;  but  the  further  we  proceed  in  this  work 
of  chemical  analysis,  the  more  individualized  appear  the  result- 
ing components.  Finally,  when  all  the  methods  for  chemical  de- 
composition now  at  our  command  have  been  exhausted,  we  arrive 
at  a  number  of  most  thoroughly  individualized  and  permanent 
substances,  which  thus  far  have  resisted  all  attempts  at  further 
decomposition ;  these  substances  are  known  as  the  Chemical 
Elements. 

A  chemical  element  is  a  substance  which,  thus  far,  has  not  been 
decomposed. 

This  our  definition  is  now*  gradually  supplanting  the  older  defi- 
nition implying  the  impossibility  of  the  further  chemical  decom- 
position of  these  elements.  It  is  of  course  very  risky  for  any  one 
man  to  assert  that  to  be  impossible  which  he  himself  is  unable  to 
do ;  but  it  is  equally  risky  for  any  one  generation  to  assert  all 
that  to  be  impossible  which  it  is  unable  to  do. 

Only  a  century  ago,  it  required  weeks  to  cross  the  Atlantic  ; 
and  no  news,  no  letter,  could  be  transmitted  between  Europe 
and  America  faster  than  the  wind  would  blow  the  best  constructed 


*  Traube,  Physik.  Cheraie,  Stuttgart,  1901,  p   27. 


sailing  vessel,  directed  by  the  most  skillful  captain,  across  the 
ocean.  Then  the  time  of  transmission  was  shortened  by  the 
introduction  of  steamships  ;  next  by  the  submarine  cable  and  now 
the  wireless  flashes  intelligence  between  shore  and  ship  in  m'd- 
ocean  and  even  across  the  broad  waters. 

As  a  matter  of  history,  many  substances  have,  at  some  given 
time,  been  classed  as  chemicial  elements,  which  now  are  known 
as  chemical  compounds.  Lavoisier  counted  the  alkalies  and 
earths  rightly  as  chemical  elements;  since  Davy  decomposed 
them  by  the  galvanic  current,  we  know  them  as  chemical  com- 
pounds, conform  to  the  supposition  of  Lavoisier. 

These  chemical  elements  are  necessarily  the  most  important  of 
all  substances  to  the  chemist,  for  all  existing  matter  is  simply  one 
or  another  of  the  infinite  number  of  combinations  or  chemical 
compounds  of  these  elements.  For  that  reason  the  physical  and 
chemical  properties  of  the  elements  have  been  one  of  the  most 
important  fields  of  study  for  the  chemist. 

But  not  all  properties  are  of  equal  importance  or  equally  char- 
acteristic. The  most  important  physical  properties  of  the 
chemical  elements  are  three,  namely,  the  specific  gravity,  the 
fusing  and  the  boiling  point.  We  shall  in  the  sequel  represent 
the  numerical  value  of  these  by  the  letters  G,  F  and  B.  Together 
these  three  constitute  the  physical  characteristic  of  an  element. 

Since  these  properties  have  definite  numerical  values  (i.  e.,  are 
quantitative  properties),  we  can  represent  them  graphically  to  the 
eye  —  and  thus  may  be  enabled  to  compare  one  element  with  an- 
other most  readily  and  most  absolutely. 

Indeed,  by  this  means  we  may  temporarily  leave  out  of  con- 
sideration all  properties  manifestly  of  secondary  value,  such  as 
color,  odor  and  the  like,  and  represent  the  most  characteristic 
properties,  or  the  real  quantitative  essence  of  the  different  elements 
by  a  system  of  points  in  space,  each  point  representing  the  three 
most  characteristic  physical  properties  exactly  in  quantity  by  its 
three  co-ordinates. 

Such  a  graphical  representation  of  a  number  of  chemical  ele- 
ments is  presented  on  plate  1. 

The  elements  themselves  are  designated  by  the  chemical  sym- 
bols introduced  by  the  founder  of  modern  quantitative  chemistry. 


Berzelius,  in  1815,  and  which  have  been  used  by  the  chemical 
world  ever  since.  These  chemical  symbols  are  composed  of  the 
initial  and  the  most  characteristic  letter  of  the  latin  or  latinized 
name  of  the  chemical  element. 

The  latin  names  of  iron,  silver,  gold  are  ferrum,  argentum, 
aurum  ;  hence  the  corresponding  chemical  symbols  are  Fe,  Ag, 
Au.  Zinc  is  latinized  zincum  ;  symbol  Zn.  Magnesium  is  desig- 
nated by  the  symbol  Mg  while  Manganese  is  represented  by  Mn. 
But  we  suppose  the  reader  to  be  familiar  with  this  part  of  chemi- 
cal notation. 

The  three  characteristic  properties  G-,  F,  B  are  in  our  chemi- 
cal books  recorded  in  tables,  and  expressed  in  numbers.  The 
numerical  unit  for  all  these  properties  is  taken  from  the  substance 
water.  The  specific  gravity  of  any  substance  being  the  weight 
in  grammes  of  one  cubic  centimeter  of  the  substance ;  the 
specific  gravity  of  water  is  one  because  the  metric  system 
takes  as  the  unit  of  weight  (the  gramme)  the  weight  of  a  cubic 
centimeter  of  water.  Again,  water  has  been  adopted  as  the 
standard  substance  for  temperature  determinations  ;  namely  its 
freezing  point  is  marked  zero,  its  boiling  point  100.  Thus,  both 
F  and  B  are  numerically  determined  on  this  thermometric  scale 
as  the  degree  (or  number)  at  which  the  solid  changes  to  a  liquid 
and  the  liquid  (under  the  pressure  of  one  atmosphere,  760  milli- 
meters of  mercury)  boils  freely. 

In  plate  1  we  lay  off  the  fusing  point,  F,  from  left  to  right, 
the  boiling  point,  B,  from  below  perpendicularly  upwards.  The 
specific  gravity  G  is  supposed  to  be  laid  off  from  the  front 
to  the  rear  horizontally;  but  in  our  diagram  we  show  it  in  the 
plane  by  an  old  form  of  perspective,  under  an  angle  of  45  de- 
grees or  half  a  right  angle.  The  words  followed  by  an  arrow, 
show  how  these  three  numerical  values  F  (to  right),  B 
(upwards)  and  G  (backwards)  are  drawn  from  the  lowest  left 
hand  point  of  the  diagram,  which  represents  the  ABSOLUTE  ZERO 
OF  TEMPERATURE  (i.  e.,  273  degrees  Centigrade  below  the  freezing 
point  of  water)  and  the  specific  gravity  zero.  That  point  is  the 
zero  point  for  the  three  co-ordinates  F  (to  right),  B  (upwards) 
and  G  (backwards,  represented  in  perspective). 

We  invite  the  reader  to  trace  this  graphical  representation  of 


the  characteristic  properties  of  a  few  of  the  best  known  groups  or 
families  of  chemical  elements.  The  trace  had  been  drawn  on  the 
horizontal  plane  (F,  G)  and  by  verticals  equal  to  the  boiling 
point  (B),  the  single  point  .in  space  representing  each  single 
element  is  determined  and  marked  by  its  chemical  symbol.  These 
points  are  joined  by  straight  lines  and  the  vertical  planes  so 
formed  are  shaded  by  perpendiculars  joining  the  line  of  points 
(opera  circles')  representing  the  element  with  the  line  of  points 
(black  circles)  representing  only  the  two  properties  (F,  G)  on 
the  horizontal  plane.  By  looking  at  this  plate  carefully  with  one 
eye  only  (the  other  being  closed)  the  broken  series  of  vertically 
shaded  plates  will  appear  standing  out  plainly  from  the  horizontal 
base  F,  G. 

For  example,  the  three  elements,  Chlorine,  Bromine  and 
Iodine  are  known  to  most  closely  resemble  one  another  chemi- 
cally, so  much  so  that  chemists  for  about  a  century  have  con- 
sidered them  to  form  a  related  group  or  family  of  chemical 
elements;  they  have  been  called  salt-formers  (or  haloids").  But 
not  all  their  compounds  are  salts,  and  many  more  compounds  are 
true  salts  that  do  not  contain  either  of  these  elements.  For  that 
reason  we  prefer  to  call  this  family  by  the  name  chloroids,  which 
simply  asserts  that  they  are  chemical  elements  closely  resembling 
chlorine  in  their  essential  properties. 

On  the  horizontal  co-ordinate  plane  F,  G,  the  three  points  rep- 
resenting these  two  properties  for  the  chioroids,  indicated  by  the 
full-shaded  black  circles  designated  Cl,  Br,  lo,  are  seen  to  lie 
exactly  in  a  straight  line.  Since  now  any  two  points  determine  a 
straight  line,  the  fact  that  the  three  points  representing  the  two 
properties  (G,  F)  of  each  one  of  these  three  elements  (Cl,  Br, 
lo)  form  one  continuous  straight  line,  proves  mathematically 
(here  geometrically)  that  these  three  elements  are  related  to  one 
another  in  some  way  in  their  essential  nature  or  composition. 
They  surely  are  not  strangers,  independent  bodies,  composed  of 
entirely  different  materials. 

From  each  point  (G,  F)  on  the  horizontal  plane  the  boiling 
point  (B)  has  been  set  off  on  its  vertical ;  the  terminals  are 
marked  by  open  circles  and  by  the  chemical  symbols  Cl,  Br,  lo. 

Here    again  we    notice  that  the  three  points    (open    circles) 


marked  Cl,  Br,  lo,  lie  in  a  straight  line,  and  in  this  case  the 
mathematical  fact  is  a  much  more  rigid  one  than  in  the  first,  be- 
cause the  angle  formed  towards  the  fusing  point  line  on  the  hori- 
zontal plane  F,  G,  is  much  more  steep  than  the  angle  of  the  latter 
towards  the  specific  gravity  axis. 

As  a  final  result,  we  find  that  the  nine  individual  determina- 
tions of  the  specific  gravity,  fusing  and  boiling  point  of  each  of 
the  three  chloroid  elements  are  not  independent  quantities,  but  are 
mathematically  related  in  such  a  manner,  that  the  three  points 
(each  representing  the  three  properties  G,  F,  B)/orm  a  straight 
line  in  space,  which  fact  is  the  geometrical  expression  of  that 
mathematical  relation. 

Another  group  of  related  chemical  elements  we  have  in  the  three 
elements:  sulphur,  selenium  and  tellurium,  which  for  conveni- 
ence we  term  the  Sulphoids,  that  is,  elements  closely  resembling 
sulphur.  On  the  horizontal  plane,  F,  G,  the  three  shaded  or 
black  circles  marked  S,  Se,  Te,  form  approximately  a  straight 
line.  Setting  off  on  perpendicularly  the  observed  boiling  points, 
we  find  the  open  circles  representing  the  three  fundamental 
properties  for  each  of  these  sulphoids,  again  in  a  straight  line. 
The  boiling  point  of  tellurium  (abt.  1400)  falls  beyond  the  mar- 
gin of  our  plate,  but  the  direction  drawn  on  our  larger  plate  is 
shown  here. 

The  two  families  of  chemical  elements  considered,  being  desti- 
tute of  metallic  properties,  are  commonly  called  Metalloids.  We 
will  now  also  examine  some  of  the  metals,  that  is  chemical  ele- 
ments possessing  metallic  luster  and  malleability  and  also  gener- 
ally being  good  conductors  of  heat  and  electricity.  The  metal- 
loids form  a  notable  contrast  with  the  metals,  not  only  in  the 
above  properties,  but  also  in  others,  that  will  be  considered 
further  on. 

First  we  will  notice  the  three  full  circles  marked  Hg,  Cd,  Zn, 
the  horizontal  plane  F,  G,  showing  that  the  fusing  point  dimin- 
ishes nearly  proportional  to  the  increase  of  the  density  —  the  very 
opposite  of  the  course  shown  for  the  metalloids  of  the  chloroid  and 
sulphoid  groups.  Setting  off  the  boiling  point  on  perpendiculars 
we  notice  the  three  points  again  in  a  straight  line  approximately, 
but  also  lowest  for  the  heaviest  metal,  that  is  reversed  in  direction 


6 

as  compared  to  the  metalloids  above  considered.  This  group  of 
three  metals  we  call  the  Cadmoids,  since  both  Zinc  and  Mercury 
closely  resemble  the  middle  member  of  the  group. 

On  this  diagram  we  have  entered  the  characteristic  properties 
(G,  F,  B)  in  the  manner  stated  (as  co-ordinates)  for  the  five 
elements,  Nitrogen,  Phosphorus,  Arsenic,  Antimony  and  Bis- 
muth, which  in  all  works  on  chemistry  for  nearly  half  a  century 
have  been  described  as  belonging  to  one  group  or  family  of 
elements;  we  have  called  this  group  the  Phosphoids,  that  is 
elements  resembling  phosphorus. 

Of  these  five  chemical  elements,  the  first  two  (N,  P)  are 
decidedly  metalloids,  while  the  last  two  (Sb,  Bi)  are  decidedly 
metals  in  every  respect  but  that  of  malleability.  In  this  regard 
antimony  and  bismuth  are  not  malleable  at  comrribn  tem- 
peratures, but  brittle,  and  sufficiently  so  that  they  may  be 
readily  pulverized  in  a  mortar.  Futhermore,  we  find  nitro- 
gen to  be  a  gas,  so  difficultly  liquefied  that  it  was  classed 
as  one  of  the  few  "  permanent  gases  "  that  up  to  1877  had  not 
been  liquefied.  Assuredly  this  group  of  chemical  elements,  the 
five  phosphoids,  comprises  elements  of  striking  variation  in  their 
characteristic  physical  properties.  It  will  therefore  be  most 
instructive  to  trace  their  place  in  our  diagram. 

We  notice,  first,  that  the  black  dots  marking  the  fusing  points 
(as  related  to  specific  gravity)  on  the  horizontal  plane  F,  G, 
form  an  approximately  straight  line  for  the  first  four  elements 
N,  P,  As,  Sb.  But  it  must  be  borne  in  mind  that  arsenic  is  so 
volatile  that  it  disappears  on  gentle  warming  in  the  open  air  with- 
out fusing;  only  when  heated  under  pressure  does  it  exhibit 
fusion,  for  pressure  increases  the  boiling  point  much  more  rapidly 
than  the  fusing  point. 

Erecting  perpendiculars  to  set  off  the  boiling  points,  we  find 
the  points  N,  P,  As,  Sb,  marked  by  open  circles,  approximately 
in  the  one  vertical  plane  P,  Sb.  They  form  a  broken  line,  in  which 
P  is  about  as  much  above  as  As  is  below  a  straight  line  drawn 
from  N  to  Sb. 

On  the  whole,  this  feature  corresponds  to  the  chloroids  and  the 
sulphoids,  that  is  to  the  metalloidic  elements.  If  we  now  from 
Sb  pass  to  Bi,  we  find  that  the  fusing  point  greatly  lowers  with 


increasing  gravity,  while  the  boiling  point  continues  to  rise  with 
increasing  gravity.  In  other  words,  compared  to  the  first  four 
phosphoids  N,  P,  As,  Sb,  the  fifth  Bi  in  its  fusing  point  changes 
like  the  metals,  while  in  its  boiling  point  it  follows  the  habit  of 
the  metalloids  thus  far  studied.  The  boiling  point  of  bismuth 
is  not  marked  on  plate  1  except  by  the  direction  of  the  arrow 
upwards  and  to  the  left  from  Sb ;  it  boils  about  1600  degrees, 
which  falls  beyond  the  range  of  our  plate. 

The  peculiar  properties  of  the  five  phosphoid  elements  furnish 
sufficient  reason  for  the  fact  that  the  first  two  (N  and  P)  by  all 
chemists  are  classed  as  metalloids,  while  the  last  three  (As,  Sb, 
Bi)  have  quite  generally  been  called  semi-metals  (Halb-Mettalle 
in  German).  The  Alchemists  were  well  acquainted  with  this 
peculiar  group  of  metals. 

On  our  plate  will  also  be  found  three  representatives  of  the 
Metals  of  the  Alkalies,  namely  Li,  Na,  Ka.  Since  such  a  name 
is  too  cumbrous  for  practical  use,  we  have  substituted  the  term 
Kaloid  for  the  same,  which  merely  implies  that  these  metals 
closely  resemble  Ka  (Kalium),  that  is  Potassium. 

It  will  be  remembered  that  we  can  represent  the  three  co- 
ordinates (G,  F,  B)  on  the  plane  of  a  diagram  only  by  means  of 
some  sort  of  perspective  drawing,  which  involves  more  or  less 
distortion.  The  mode  of  perspective  selected  by  us  and  used  in 
the  diagram  we  have  thus  far  studied,  gives  the  two  temperatures 
(F  and  B)  in  true  dimensions,  without  any  distortion,  but  the 
specific  gravity  G  then  necessarily  is  greatly  distorted  in  direc- 
tion. 

If  we  would  have  the  entire  representation  without  distortion 
we  must  make  three  drawings  instead  of  one,  namely  one  each  for 
the  three  co-ordinate  planes  G,  F ;  F,  B  and  G,  B  —  and  then 
mentally  combine  these  three;  or  we  must  represent  them  in  a 
bodily  model. 

Such  a  model  can  be  readily  constructed  by  taking  plane  G, 
F  as  the  base,  and  erecting  perpendiculars  of  proper  lengths 
(say  of  wires  or  wood)  inserted  in  the  points  marking  the  fusing 
point.  The  lines  in  space  then  can  be  marked  by  wires,  threads 
or  narrow  ribbons  of  different  colors.  Such  a  model  shows 
almost  at  a  glance  many  general  laws  of  great  importance  that* 


8 

have  been  entirely  overlooked  by  chemists  who  have  merely  put 
the  observed  data  in  columns  of  printed  tables  in  their  books. 

Plate  2  gives  the  base  for  such  a  model ;  it  represents  the 
gravity  and  fusing  point,  that  is  the  plane  G,  F.  We  have 
also  added  our  symbol  for  the  genera  or  groups  of  chemical  ele- 
ments, namely  the  Greek  letters  corresponding  to  the  Latin  intro- 
duced by  Berzelius  for  the  individual  elements. 

Since  for  typographical  reasons  we  cannot  insert  these  our  Greek 
group-symbol,  in  the  text,  we  have  marked  them  on  the  plates 
only.  The  symbol  for  the  chloroids  is  pronounced  chi,  for  the 
sulphoids  theta,  for  the  phosphoids  phi,  for  the  cadmoids  Kappa- 
delta,  and  for  the  Kaloids  Kappa-alpha. 

In  this  plate  both  specific  gravity  and  fusing  point  are  repre- 
sented without  distortion.  We  notice  the  Chloroids  (Cl,  Br,  lo) 
and  Sulphoids  (S,  Se,  Te)  as  well  as  the  first  four  Phosphoids 
(N,  P,  As,  Sb),  showing  that  the  fusing  point  rises  with  the  spe- 
cific gravity,  which  we  above  have  found  to  be  a  peculiarity  of 
metalloids.  The  three  Cadmoids,  Hg,  Cd,  Zn,  show  the  opposite 
character,  their  line  of  fusing  points  standing  almost  at  right 
angles  to  that  of  the  metalloids  just  specified. 

Modern  chemists  quite  generally  include  magnesium  (Mg)  and 
Beryllium  (Be)  with  the  above  Cadmoids;  our  diagram  shows 
that  the  line  of  fusion  continues  downward  and  almost  in  the 
same  direction  from  Zn  to  Be  as  from  Hg  to  Zn. 

On  this  chart  it  has  been  possible  also  to  locate  the  metals, 
Copper,  Silver  and  Gold,  which  we  designate  as  Cuproids,  i.  e., 
Copper-like  metals.  It  will  be  noticed  that  the  line  of  fusing 
points  of  the  cuproids  neither  goes  down  with  decreasing  specific 
gravity  as  for  the  metals,  nor  up,  as  for  the  metalloids;  in  fact 
it  remains  very  nearly  the  same  for  Cu,  Ag  and  Au,  although  the 
specific  gravity  varies  more  than  in  the  ratio  of  one  to  two. 

This  fact  should  cause  us  to  think  twice  before  we  generalize 
our  conclusions,  making  the  contrast  between  metal  and  metal- 
loids. Surely  the  Cuproids  possess  the  physical  properties  of  the 
metals  in  the  highest  degree.  We  must  therefore  inquire  what 
may  be  the  cause  here  involved,  marking  the  contrast  between, 
say,  Chloroids  and  Cadmoids,  with  Cuproids  as  the  connecting 
link. 


9 

A  moment's  consideration  will  suffice  to  recognize  that  metals 
are  of  two  kinds  in  their  electrical  character,  as  determined  by 
their  deportment  in  the  electrolysis  of  their  compounds.  We  may 
be  pardoned  to  retain  the  nomenclature  of  the  founder  of  quanti- 
tative chemistry  and  really  also  of  electrochemistry;  we  shall, 
then,  with  Berzelius,  continue  to  call  that  constituent  electro- 
positive which  in  electrolysis  appears  at  the  negative  electrode, 
and  shall  likewise  call  that  constituent  electronegative  which  in 
electrolysis  appears  at  the  positive  electrode. 

Now,  the  cadmoids  are  pronounced  electropositive  metals ;  so 
are  still  more,  the  kaloids.  The  metalloids  are  electronegative ; 
the  cuproids  are  comparatively  neutral. 

Accordingly  we  may  express  the  rules  above  stated,  defin- 
ing the  relation  of  the  fusing  point  to  the  specific  gravity,  in  the 
following  manner :  — 

1.  The  fusing   point  of   pronounced   electronegative  elements 
increases  with  their  specific  gravity.     Examples  :  the  Metalloids  ; 
Chloroids,  Sulphoids. 

2.  The  fusing   point  of   pronounced   electropositive    elements 
diminishes   with   increasing    specific   gravity.     Examples:   Cad- 
moids, Kaloids. 

3.  The  fusing  point  of  intermediate   (relatively  neutral)  ele- 
ments does  not  vary  notably  with  their  specific  gravity.     Exam- 
ple:  Cuproids. 

THE    BOILING-FUSING    POINTS. 

It  will  also  prove  very  interesting  and  quite  instructive 
to  study  our  plane  B  F,  that  is  the  fusing-boiling  points 
of  the  elements.  Here  each  element  (or  generally  substance) 
is  again  represented  by  a  single  point,  the  abscissa  of 
which  is  the  fusing  point,  while  the  ordinate  is  the  boiling 
point.  Of  such  diagrams  my  chemical  atlas  (size  double  ele- 
phant drawing  paper)  contains  a  number ;  plate  3  is  a  greatly 
reduced  copy  representing  the  boiling-fusing  points  of  the 
chemical  elements. 


10 

The  origin  is  the  absolute  zero,  but  the  temperatures  are 
plotted  by  the  more  convenient  centigrade  degrees,  thousand 
degrees  to  71  millimeters.  The  fusing  points  covered  by  this 
plate  reach  about  1100  C.,the  boiling  points  about  1600  C.,  so 
that  the  total  range  for  these  (from  absolute  zero)  is  about  1400 
and  1900  degrees.  For  a  number  of  very  interesting  elements, 
the  boiling  point  falls  above  the  limit  of  the  plate  ;  if  the  fusing 
point  is  known  and  below  1100  degrees,  it  is  entered  on  the  1500 
degree  line,  and  marked  by  an  arrow  pointing  "upwards" 
towards  the  boiling  point  beyond  the  limit  of  the  plate. 

I  do  not  know  that  such  charts  or  diagrams  have  been  used 
by  others  in  the  study  of  the  change  of  state  of  aggregation  of 
chemical  compounds  and  elements ;  but  I  know  that  such  dia- 
grams have  aided  me  greatly  in  the  study  of  the  mechanical 
conditions  of  the  change  of  state  of  aggregation,  which  investi- 
gation has  been  carried  on  by  me  for  many  years,  as  evidenced 
by  my  list  of  publications. 

We  see  here  at  a  glance  (plate  3)  that  the  boiling-fusing  point 
curve  for  the  chloroids  and  kaloids  is  a  straight  line,  also  for  the 
first  four  phosphoids  ;  that  it  is  approximately  a  straight  line  for 
the  sulphoids  and  cadmoids.  These  groups  of  elements  are  desig- 
nated near  the  curve  by  our  Greek  symbol  of  the  same,  while  the 
individual  elements  are  designated  by  their  chemical  symbol  in- 
troduced by  Berzelius.  The  boiling-fusing  point  of  nitrogen  is  a 
little  below  the  straight  line  determined  by  Sb — P  ;  but  the  boil- 
ing-fusing point  of  fluorine  has  been  found  a  corresponding  small 
number  of  degrees  above  the  straight  line  determined  by  Cl — 
Br — lo.  Finally  it  will  be  noticed  that  the  boiling-fusing  point 
of  hydrogen  is  quite  near  the  absolute  zero. 

It  is  very  much  to  be  regretted  that  experimental  determina- 
tions are  still  very  incomplete,  allowing  us  only  to  represent  about 
half  a  dozen  genera  (or  families)  of  chemical  elements  on  this 
diagram. 

The  angle  under  which  the  straight  line  or  nearly  straight  line 
of  boiling-fusing  points  of  a  genus  of  elements  inclines  towards 
the  horizontal  (abscissa)  marks  the  ratio  at  which  boiling  and 
fusing  points  increase  for  a  given  genus  or  group  of  elements. 
Thus,  for  the  chloroids  the  angle  is  near  45  degrees,  showing  an 


11 

approximately  equal  increase  in  both  temperatures,  while  for  the 
sulphoids  and  kaloids  the  angle  is  nearly  70  degrees,  showing 
that  the  change  in  boiling  point  is  much  greater  than  the  corre- 
sponding change  in  fusing  point. 

But  this  is  not  the  place  to  enter  upon  the  finer  details,  though 
they  are  exceedingly  important  and  interesting;  they  must  be 
looked  up  in  our  special  publications  on  this  subject.  Here  we 
merely  intend  to  present  a  popular  outline  of  our  results. 

In  this  connection  we  may  also  state  that  we  do  not  want  to 
present  the  numerical  data  —  which  may  be  found  in  any  modern 
work  on  chemistry  or  physics  —  but  we  present  these  data  in 
graphical  form,  in  diagrams,  most  carefully  and  accurately  con- 
structed on  a  large  scale,  using  ordinarily  a  sheet  of  the  size 
known  as  double  elephant ;  from  these  large  and  accurate  draw- 
ings, the  cuts  inserted  in  this  work  have  been  obtained  by 
photography.  They  are  therefore  almost  microscopically  exact. 

Again  for  a  moment  returning  to  the  consideration  of  our  plate 
3,  we  notice,  by  the  chemical  symbols  inscribed  near  the  points 
in  the  boiling-fusing  point  lines,  that 

1.  For   electronegative    elements   (Chloroids,  Sulphoids)   the 
boiling-fusing  point  lines  run  upwards  with  increasing  density  ; 
while 

2.  For  pronouncedly  electropositive  elements  (Kaloids,  Cad- 
moids)  the  boiling-fusing  point  line  runs  downwards  with  increas- 
ing density. 

The  intermediate  class  of  chemical  elements  (Cuproids)  are  not 
represented  on  this  diagram,  because  their  boiling  points  fall  be- 
yond the  limits  of  this  plate,  and  are  not  known  with  sufficient 
precision. 

THE    ATOMIC    WEIGHTS    OF    THE    ELEMENTS. 

Thus  far  we  have  exclusively  used  the  three  fundamental  char- 
acteristics G,  F,  and  B  of  the  chemical  elements.  These  three 
are  all  truly  physical  properties.  We  have,  however,  grouped 
some  of  the  elements  in  accordance  with  the  chemical  experience 


12 

of  almost  a  century.  As  examples  we  refer  to  the  chloroids,  the 
kaloids,  and  other  groups  of  elements  specified. 

But  it  is  well  known  that  the  physical  characteristic  (G)  called 
the  specific  gravity  is  variable  with  temperature,  usually  dimin- 
ished as  the  temperature  increases. 

Accordingly  it  may  not  bring  out  the  true  relations  in  the  most 
perfect  manner.  Thus  in  our  diagram  Plate  1  we  find  the  fusing 
points  of  Cl,  Br,  lo  apparently  in  a  straight  line.  But  when  the 
same  data  were  constructed  without  the  angular  distortion  of 
perspective  (see  Plate  2),  we  notice  a  slight  break  in  the  line 
Cl — Br — lo.  Now  the  question  arises:  is  this  slight  differ- 
ence in  the  direction  Cl — Br  from  that  of  the  direction  Br — lo 
real,  or  is  it  merely  apparent,  due  to  the  above  admitted  variation 
of  the  specific  gravity  with  temperature  ? 

In  earlier  efforts  on  this  ground  attempts  have  been  made  to 
apply  corrections  to  the  values  of  specific  gravities  or  to  reduce 
the  same  to  some  definite  degree  of  temperature,  or  to  some  tem- 
perature a  certain  number  of  degrees  distant  from  the  fusing 
point.  All  such  endeavors  are  unsatisfactory,  because  they  in- 
troduce new  unknown  or  uncertain  data. 

But  chemists  know  that  the  physical  property  called  the  specific 
gravity  for  related  chemical  elements  varies  with  the  atomic  iveight 
of  such  elements ;  and  since  this  atomic  weight  is  entirely  inde- 
pendent of  temperature  and  other  physical  conditions,  it  appears 
desirable  to  introduce  the  same  in  place  of  the  specific  gravity  in 
charts  for  the  study  of  boiling  and  fusing  points  of  the  chemical 
elements. 

We  therefore  must  try  this  method  of  comparison,  i.  e.,  the 
replacement  of  the  somewhat  variable  specific  gravity  by  the 
invariable  atomic  weight  of  the  chemical  elements. 

But  if  we  turn  to  the  more  recent  chemical  publications  we  find 
that  the  atomic  weights  of  the  chemical  elements  have  become 
entangled  in  the  meshes  of  authority  and  technicality.  In  the 
United  States,  the  Smithsonian  Institution  has  put  its  stamp  of 
authority  upon  a  set  of  values  professedly  calculated  with  great 
mathematical  precision.  These  American  Government  authori- 
ties (for  the  professed  calculator  is  an  officer  of  the  Department 
of  the  Interior)  have  combined  with  the  American  Chemical 


13 

Society  and  with  certain  representatives  of  the  German,  English 
and  French  Chemical  Societies,  in  issuing  annually  a  set  of  Inter- 
national Atomic  Weights  for  the  universal  use  of  the  chemists  of 
the  world. 

These  so-called  international  atomic  weights  have  not  been 
universally  adopted  by  the  chemists  of  the  world.  The  fixing 
of  definite  scientific  values  by  agreement  of  certain  so-called 
international  authorities  seems  to  be  as  futile  to-day  as  corre- 
sponding decrees  on  scientific  fundaments  have  proved  them- 
selves in  former  centuries. 

We  only  mention  these  facts  and  circumstances  here  at  this 
point  to  advise  the  reader  that  we,  in  this  our  study,  cannot  use 
these  so-called  international  atomic  weights  because  we  have 
found  them  to  be  not  true  to  nature,  but  incorrect  and  false  in 
most  essential  particulars. 

We  shall  substantiate  this  statement  in  the  closing  part  of  this 
small  work ;  here  it  will  be  perfectly  sufficient  to  use  our  own 
atomic  weights,  which  are  essentially  the  same  as  those  in  common 
use  before  this  official  declaration  of  natural  values  was  under- 
taken. This  is  so  much  the  more  proper,  as  the  differences 
between  or  own  (or  the  old)  atomic  weights  and  the  so-called 
international  atomic  weights  are  numerically  so  small  as  not  to 
affect  the  results  of  our  conclusions  in  this  present  research. 

Since  these  so-called  international  atomic  weights  are  being  used 
to  support  a  false  chemical  principle  and  since  they  have  been 
proved  to  be  false  in  themselves,  it  will  be  impossible  for  us  to 
use  the  same.  See  our  "  True  Atomic  Weights,"  1894,  and 
especially  our  "  Absolute  Atomic  Weights,"  1901. 

The  atomic  weights  are  supposed  to  be  implicitly  represented 
in  the  symbol  of  the  chemical  elements.  We  give  a  few  examples : 
H,  1;  O,  16;  C,  12;  Li,  7;  Na,  23;  Ag,  108;  Fe,  56;  Ca, 
40  ;  As,  75  ;  N,  14  ;  etc.,  etc.  We  do  not  need  to  burden  these 
pages  with  a  full  table  of  atomic  weights. 

We  will  merely  add,  for  information,  that  for  the  above  elements, 
the  so-called  "  international  atomic  weights  "  proclaimed  for  the 
year  1902  were  in  the  order  above  used :  1.008;  12.00;  7.03; 
23.05;  107.93;  55.9;  40.1;  75.0;  14.04.  What  the  precise 
values  decreed  for  1904  may  be,  1  have  not  taken  the  trouble  to 


14 

look  up,  for  the  pretendedly  ascertained  and  proclaimed  small 
differences  of  these  so-called  international  atomic  weights  from 
the  old  or  common  atomic  weights  above  given  and  here  to  be 
u^ed,  are  insignificant  for  our  present  and  for  most  practical 
purposes. 

Taking  now  the  common  atomic  weights  as  abscissae  (instead 
of  the  specific  gravity)  and  the  temperature  in  Centigrade  degrees 
as  ordi nates,  we  obtain  the  diagram  Plate  4,  in  which  the  fusing 
points  are  marked  by  full,  black  circles,  and  the  boiling  points 
by  open  circles.  It  might  have  been  advisable  to  represent  these 
two  values,  B  and  F,  on  two  distinct  diagrams  ;  but  our  diagram 
giving  both,  while  a  little  more  complex,  has  the  great  advantage 
of  permitting  a  direct  comparison  of  the  course  of  fusing  points 
with  that  of  the  boiling  points  for  any  group  of  chemical  elements. 

Our  diagram,  Plate  4,  graphically  represents  the  Boiling 
and  Fusing  Points  of  the  Chemical  Elements  in  Relation  to  tln'ir 
Atomic  Weight.  The  temperature  runs  up  from  the  absolute 
zero  to  1600  degrees  Centigrade,  and  the  atomic  weight  from 
zero  to  about  230.  The  temperatures  of  0,  500,  1000  and  1500 
degrees  are  marked,  also  the  atomic  weights  0,  100,  200.  The 
original  drawing  was  made  most  carefully  on  a  half-sheet  of 
double  elephant  drawing  paper,  and  reduced  photographically  to 
ths  diagram  here  inserted,  which  therefore  is  almost  microscopic- 
ally exact.  It  will  bear  the  use  of  an  ordinary  magnifying  glass. 
It  will  be  advisable  to  study  first  the  fusing  point  lines  (black 
circles)  and  thereafter  the  boiling  point  lines  (open  circles)  ;  for 
the  former  are  necessarily  most  complete,  since  many  boiling 
points  fall  above  the  limit  of  our  diagram. 

FUSING    POINTS    AND    ATOMIC    WEIGHTS. 

First,  we  notice  the  fusing  line  of  the  chloroids  Cl — Br — lo 
to  form  practically  a  straight  line ;  the  fusing  point  of  Br  being 
but  very  little  below  the  straight  line  joining  Cl  and  lo,  so  little 
that  it  takes  a  good  eye  to  see  the  slight  break  at  Br. 

Second,  for  the  denser  and  less  volatile  sulphoids  the  deviation 
of  Se  from  the  straight  line  indicated  by  the  points  8 — Te  is 


15 

considerable.  The  fusing  point  of  tellurium  is  considerably 
higher  than  would  be  indicated  by  the  prolongation  of  the  straight 
line  S  — Se. 

Third,  for  the  corresponding  phosphoids  P — As — Sb  the 
deviation  is  in  the  opposite  direction,  for  the  fusing  point  of  Sb 
lies  below  the  straight  line  drawn  from  P  to  As  and  continued. 

For  all  these  elements  (chloroids,  sulphoids,  phosphoids)  the 
fusing  line  runs  obliquely  upwards. 

The  steepness,  or  the  angle  formed  between  the  fusing  line  and 
the  horizontal  is  least  for  the  chloroids,  greatest  for  the  phos- 
phoids, intermediate  for  the  sulphoids.  In  other  words,  while  the 
fusing  points  for  all  these  groups  INCREASES  with  the  atomic 
weight,  this  increase  is  greatest  for  the  phosphoids,  least  for  the 
chloroids  and  intermediate  for  the  sulphoids,  for  an  equal  increase 
of  the  atomic  weight. 

This  is  a  most  remarkable  fact  which  immediately  suggests  a 
relation  to  the  chemical  valence  of  these  elements.  It  will  be 
remembered  that  one  atom  of  chlorine  is  saturated  by  one  atom 
of  hydrogen,  but  that  the  saturation  of  one  atom  of  sulphur 
requires  two  atoms  of  hydrogen,  while  one  atom  of  phosphorus 
requires  three  atoms  of  hydrogen  for  saturation, 

Accordingly,  the  valence  of  the  chloroids  is  one,  that  of  the 
sulphoids  is  two,  while  the  phosphoids  have  the  valence  three. 
This  is  manifestly  the  order  of  steepness  of  their  fusing  point  line 
brought  out  by  our  diagram. 

Taking,  as  a  first  approximation,  the  straight  line  determined 
by  the  first  and  last  of  the  three  elements  of  each  of  these  groups, 
a  simple  measurement  on  the  original  drawing  gives  for  the  angle 
of  elevation  in  question  the  following  values,  in  degrees: 

Chloroids  25  ;  sulphoids  36  ;  phosphoids  53  ;  for  which  the 
natural  tangents  are  respectively  0.47,  0.73  and  1.33,  which 
means : 

For  an  increase  of  one  hundred  in  the  atomic  weight,  the  fusing 
point  rises  for  chloroids  47  degrees,  for  sulphoids  73  and  for 
phosphoids  1$3  degrees. 


16 

If  we  divide  this  rise  by  the  valence  of  the  element,  we  obtain 
per  hundred  atomic  weight  and  per  valence  one  an  increase  of 
the  fusing  point  of 

47  degrees  for  chloroids, 
36  "  "  sulphoids, 
44  "  "  phosphoids. 

These  values  are  nearly  equal,  when  we  consider  that  we  have 
taken  only  the  general  trend  of  the  fusing  point  lines  as  marked 
by  the  first  and  last  members  of  these  groups  of  three  elements  — 
the  triads  of  Doebereiner.  1829. 

The  mean  of  these  values  is  42.  Our  diagram  therefore 
proves  that  the  fusing  jwint  of  the  most  electro  if 'j«tn-<>  de- 
ments rises  about  42  degrees  for  each  unit  of  valence  per  one 
hundred  units  of  the  atomic  weight  in  the  triads  Cl — Br— lo; 
S— Se— Te;  P— As— Sb. 

If  we  now  look  below  and  above  these  middle  terms  —  the  old 
triads  —  we  find  most  important  new  facts. 

First,  the  line  from  Cl,  S,  P  to  the  initial  element  (Fl,  O,  N) 
of  the  genus  or  family  considered,  is  not  in  line  with  that  of  the 
triad,  but  very  much  steeper,  showing  a  sharp  break  or  elbow  at 
the  first  element  (Cl,  Br,  lo)  in  the  triad. 

This  mathematical  relation  exhibited  geometrically  in  our 
graphical  representation  demonstrates  with  absolute  certainty 
that  the  starting  member  of  a  genus  is  not  in  its  composition  or 
structure  identical  with  the  next  three  members  which  constitute 
the  old  triad. 

It  is  true,  our  diagram  gives  only  the  exact  location  of  the 
fusing  points  of  hydrogen  and  nitrogen  ;  but  we  know  that  the 
fusing  points  of  oxygen  and  fluorine  are  within  the  small  area 
determined  by  these  two,  which  fact  is  sufficient  to  fix  the  direc- 
tion of  the  lines  from  P,  S,  and  Cl  in  question,  and  which  lines 
are  properly  dotted  on  our  diagram  for  S  and  Cl  while  the  line 
from  P  to  N  is  drawn  and  in  full,  having  been  experimentally 
determined  when  the  diagram  was  drawn  by  us.  To-day,  the 
experimental  data  for  the  others  also  having  been  determined,  we 
might  enter  the  same  on  a  new  diagram ;  but  it  is  evident  that  it 


17 

would  produce  no  visible  difference  on  the  resulting  new  chart. 
We  have  neither  the  time  to  make  such  new  chart  nor  the  money 
to  pay  for  a  new  cut  that  is  not  necessary. 

Next  we  will  look  at  the  related  element  beyond  the  triad. 
Here  we  find  only  one  case,  namely  bismuth  of  the  phosphoid 
group,  for  the  long  espected  heavier  fifth  element  of  the 
chloroid  and  sulphoid  groups  have  not  yet  been  found. 

The  fusing  line  Sb — Bi  is  seen  to  turn  downwards,  almost  at 
right  angles  to  the  general  direction  of  the  fusing  line  P — Sb. 
My  original  drawing  shows  this  angle  to  be  89  degrees. 

The  diagram  Plate  4  shows  the  fusing  line  Sb — Bi  of  the 
phosphoids  to  be  exactly  parallel  to  the  tline  Cd — Hg  of  the 
cadmoids  ;  on  my  original  large  drawing  this  parallelism  obtains 
perfectly  when  tested  by  proper  means. 

This  fact  not  only  proves  again  the  metallic  character  of  the 
last  two  phosphoids,  but  also  shows  that  the  constitution  of  Bi 
must  differ  from  that  of  the  triad  P,  As,  Sb. 

Passing  now  to  the  consideration  of  the  fusing  points  of  the 
metals,  we  naturally  begin  with  the  most  marked  of  all  metallic 
genera,  the  most  electropositive  of  all  elements  of  lowest  valence 
(one)  of  all,  also  the  most  volatile  and  fusible  of  all  metals,  fin- 
ally the  lightest  of  all  metals,  the  kaloids:  Li,  Na,  Ka,  Rb,  Cs. 
This  genus  or  family  of  elements  is  as  absolutely  fixed  and  lim- 
ited as  that  of  the  monovalent,  most  electronegative  metalloids, 
the  chloroids. 

Our  diagram  shows  that  the  fusing  point  line  sets  in  highest 
with  lithium,  and  gradually  runs  down  to  the  lowest  fusing  point 
of  the  heaviest  cesium.  While  the  total  range  in  fusing  point  for 
the  kaloids  is  much  less  than  that  for  the  chloroids,  there  can  be 
no  question  about  the  fact  that  it  runs  in  the  opposite  direction : 
falling  instead  of  rising  with  increasing  atomic  weight. 

The  divalent  metals  form  the  genus  of  cadmoids,  comprising 
Be,  Mg,  Zn,  Cd,  Hg.  The  range  in  fusing  point  is  much  greater, 
the  fusing  point  line  running  down  much  faster  from  Be  (about 
1000  degrees)  to  Hg  (below  zero). 

The  line  shows  plainly  two  divisions,  namely  the  steepest  de- 
scent from  Be  to  Zn,  followed  by  a  much  more  gradual  descent 
from  Zn  to  IJg. 


18 

The  trivalent  genus  Bo,  Al,  Ga,  In,  Tl  which  we  have  called 
the  styptoids  after  aluminum,  starts  its  fusing  point  line  with 
boron  beyond  the  field  covered  by  our  chart,  above  1600  degrees, 
falls  most  rapidly  down  to  Mg  (about  700)  drops  once  more  to 
Ga  and  then  leisurely  rises  over  In  to  Tl. 

The  tetravalent  genus  C,  Si,  Ge,  Sn,  Pb  which  we  have  called 
Adamantoids  after  the  diamond,  shows  a  similar  fusing  point 
line. 

That  the  descent  of  fusing  point  for  the  metals  is  related  to  the 
valence  in  a  like  manner  as  we  found  the  ascent  of  the  fusing 
point  for  the  metalloids  there  can  be  no  question,  for  the  diagram 
shows  it  unmistakably  ;  the  descent  is  slowest  for  the  monovalent, 
much  more  rapid  for  the  divalent  and  most  steeply  descending 
for  the  tri-  and  tetravalent  elements. 

In  the  main,  the  numerical  relations  may  also  be  detected. 
The  line  Li — Na  meets  the  base  under  an  angle  of  49.5  degrees, 
the  tangent  of  which  is  1.15.  The  line  Be  —  Zn,  on  which  Mg  is 
found,  meets  the  base  under  the  angle  of  63.5  of  which  the  tan- 
gent is  2.00.  This  is  sufficiently  near  the  proportion  of  1  to  2 
of  the  valence  for  kaloids  and  cadmoids,  considering  the  intricacy 
of  the  problem. 

For  the  next  two  genera  of  elements  the  conditions  are  more 
complex.  The  first  element  of  the  divalent  cadmoids  is  still 
properly  a  metal,  namely,  Beryllium.  But  the  first  member  of 
the  trivalent  genus  is  Boron,  of  the  tetravalent  it  is  Carbon,  and 
neither  of  these  elements  can  be  considered  metallic  in  character. 
Only  the  second  member  (Al,  Ge)  may  be  taken  as  metallic. 

Now,  as  we  found  a  change  in  fusing  point  relations  when  from 
metalloid  we  passed  to  metallic  members  in  the  electronegative 
genera,  so  we  must  expect  here  varying  relations  where  we 
pass  from  the  metallic  to  the  truly  non-metallic  electronegative 
elements. 

Nevertheless,  the  effect  of  valence  on  fusing  point  variation  is 
plainly  marked,  as  the  following  facts  will  show. 

For  the  trivalent  elements,  the  inclination  Bo — Al  to  the  horizon- 
tal being  85  degrees,  the  tangent  of  which  is  11.4,  shows  plainly 
a  transition.  Taking  the  next  member,  the  line  Al — Ga  inclines 
at  73  degrees,  of  which  the  tangent  is  3.27.  This  corresponds 


19 

to  Mg — Zn,  which  inclines  63.5  degrees,  of  which  the  tangent 
is  2.00. 

For  the  tetravalent  elements  the  inclination  C — Ge  to  the  hori- 
zontal is  78  degrees,  of  which  the  tangent  is  4.7.  But  for  the 
second-third  elements  Ge — Sn  the  inclination  63  gives  only  1.96 
as  tangent ;  evidently  we  get  here  no  comparable  result,  tin  being 
too  different  from  Carbon  and  Germanium ;  some  chemists  even 
doubt  its  place  in  this  genus. 

Making  all  due  allowance  for  the  influence  of  the  transition 
from  true  metals  to  metalloids,  we  can  tabulate  the  fall  of  the 
fusing  point  for  an  increase  of  hundred  units  in  the  atomic 
weight  for  the  first  members  of  the  four  genera  of  electropositive 
elements  in  the  following  manner :  — 

Valence,  1234 

Fall  degrees,  115  200  327  470 

Per  unit  valence,       115  100  109  117 

The  mean  of  these  values  is  110  degrees,  which  may  be  taken 
as  the  fall  of  the  fusing  point  per  unit  of  valence  produced  by  a 
rise  of  one  hundred  units  in  the  atomic  weight  for  the  first  mem- 
bers of  any  one  genus  of  the  electropositive  elements. 

The  corresponding  rise  for  the  middle  triad  of  the  electro- 
negative genera  of  elements  we  found  to  be  42 .  But  strictly  this 
rise  cannot  be  compared  in  amount  with  the  fall  for  the  first 
members  of  the  electropositive  elements. 

Our  diagram  gives  the  fusing  point  line  N — P  from  observa- 
tion ;  this  only  is  comparable  to  the  fall  for  the  electropositive  ele- 
ments. Let  us  determine  it. 

Direct  measurement  on  our  original  drawing  shows  that  the 
line  N — P  forms  an  angle  of  73  degrees  with  the  horizontal ;  the 
tangent  hereof  is  3.27,  giving  a  rise  of  327  degrees  in  fusing  point 
per  hundred  increase  in  atomic  weight.  Since  these  elements  are 
trivalent,  the  rise  is  109  degrees  per  unit  valence. 

This  agrees  with  the  corresponding  fall  for  the  electropositive 
elements,  being  in  fact  identical  with  that  for  the  elements  Al — 
Ga. 

We  may  now  consider  the  course  of  the  fusing  point  lines  for 


20 

last  members  of  each  of  these  genera  of  electropositive  elements. 
For  the  Kaloids  and  Cadmoids  we  have  already  traced  the  con- 
tinuous obliquely  downward  course  of  these  lines.  But  the 
other  two  lines  terminate  in  an  upwards  course  forming  an  elbow 
respectively  at  Ga  for  the  Styptoids  and  at  Sn  for  the  Adaman- 
toids.  We  also  notice  that  this  rise  is  not  greatly  different  from 
that  of  the  chloroids,  though  somewhat  less.  The  lines  Sn — Pb 
and  In — Tl  are  practically  parallel.  Also  In — Tl  is  practically 
perpendicular  to  Al — Ga. 

This  corresponds  exactly  to  the  turn  under  a  right  angle  of 
Sb — Bi  to  P — Sb,  brought  out  when  we  studied  the  fusing  point 
lines  of  the  metalloids. 

Measurement  gives  the  inclination  of  the  line  Sn — Pb  17  de- 
grees, while  In — Tl  is  found  to  be  14  degrees,  the  mean  is  15.5 
degrees,  of  which  the  tangent  (i.  e.,  rise  per  unit)  is  0.28.  The 
number  of  degrees  the  fusing  point  rises  for  these  metals  for  an 
increase  of  hundred  units  of  their  atomic  weight  is  therefore  28. 

Finally  our  chart  shows  the  fusing  point  lines  for  two  triads  of 
intermediate  elements  or  metals,  namely  the  Cuproids  and 
Palladoids.  These,  as  stated  before,  show  no  great  change  in 
fusing  point ;  the  line  Cu — Au  rising  at  an  angle  of  1  degree 
only,  corresponding  to  a  change  of  only  2  degrees  in  the  fusing 
point  per  100  atomic  weight. 

To  complete  the  inquiry,  we  find  the  rise  of  the  line  Ag — Au 
14  degrees,  the  tangent  of  which  is  0.25.  Thus  from  silver  to 
gold  the  fusing  point  rises  25  degrees  per  hundred  increase  in 
atomic  weight.  This  line  is  exactly  parallel  to  the  line  In — Tl 
and  differs  but  little  in  direction  from  the  line  Sn — Pb  (incl.  17 
degrees,  tangent  0.31)  and  Pd — Pt  (incl.  18  degrees,  tangent 
0.33). 

But  while  the  terminal  part  of  these  lines,  closing  with  the 
element  of  highest  atomic  weight,  are  nearly  parallel,  thereby 
showing  rise  of  between  25  and  33  degrees  in  the  fusing  point 
for  an  increase  of  100  in  the  atomic  weight,  the  preceding  line 
meets  this  terminal  line  under  a  very  different  augle. 

Our  diagram  shows  the  angle  at  Pd  and  Ag  to  be  quite 
obtuse  —  about  150  degrees  at  Pd,  141  degrees  at  Ag ;  at  Sn 
the  corresponding  angle  is  110  only.  These  facts  amplify  the 


21 

evidence  obtained  before  showing  that  the  cuproids,  being  elec- 
trically intermediate,  must  be  considered  as  forming  an  interme- 
diate and  distinct  division  of  the  elements.  The  palladoids  here 
show  themselves  to  possess  the  same  characteristics  in  their 
fusing  point  line  both  as  to  position  (high  up)  and  as  to  form 
(nearly  a  straight  line). 

Before  passing  to  the  consideration  of  the  boiling-point  lines 
represented  on  this  diagram,  we  shall  sum  up  the  general  facts 
ascertained  for  the  fu sing-point  lines. 

1.  The  fusing -point  line  for  any  one  genus  of  chemical  elements 
consists  of  three  distinct  parts,  namely  :  — 

an  initial  part,  very  steep ; 
a  middle  part,  moderately  inclined  ; 
and  a  terminal  part. 

2.  For  the  electro-negative  elements  (metalloids),  the  fusing 
point   line   rises,    for  the   pronounced  electro-positive  (metallic) 
elements  it  falls  with  increasing  atomic  weight,  while  for  less  pro- 
nounced  elements  (like  the  cuproids)  there   is   but  a  moderate 
change. 

3.  The  initial  part  shows  an  almost  equal  change  —  rise  for 
metalloids,    fall   for   metals — for   a    unit   of    valence  and   per 
hundred  increase  in  atomic  weight. 

4.  For  the  middle  part  —  the  old  triads  —  the  change  per  unit 
valence  and  hundred  units  of  atomic  weight  is  also  the  same,  but 
less  than  half  the  initial  amount. 

Now,  turning  to  the  consideration  of  the  boiling  point  lines,  we 
first  notice  with  regret  the  paucity  of  material  at  hand,  largely 
due  to  the  generally  high  boiling  points  of  the  majority  of  the 
elements,  which  have  offered  great  obstacles  to  experimental 
determinations.  Possibly  the  recently  introduced  method  of 
boiling  metals  in  an  almost  absolute  vacuum  may  yield  valuable 
data,  if  strictly  comparable  conditions  can  be  secured. 


22 


From  the  data  at  hand  when  our  diagram  Plate  4  was  drawn, 
we  have  only  constructed  the  lines  for  the  Argonoids,  Chloroids, 
Sulphoids,  Phosphoids,  Kaloids  (very  incomplete)  and  Cad- 
inoids. 

First,  we  notice  that  boiling  point  lines  of  the  Kaloids 
and  Cadmoids  show  the  same  contrast  with  that  of  the  electro- 
negative metalloids  as  did  the  fusing  point  lines :  risiny  with 
increase  of  atomic  weight  for  the  metalloids,  falling  for  the 
metals. 

Second,  we  see  most  markedly  the  initial  and  middle  part  of 
these  lines  to  be  totally  distinct,  the  first  much  more  steep  than 
the  second.  This  feature  is  even  shown  by  the  nullovalent 
elements,  the  argonoids. 

The  following  table  shows  the  principal  results  that  may  be 
read  off  from  our  diagram : 


Genus.                     Part. 

Inclination. 

Tangent. 

Argonoids  :     Initial,      He  —  Ar 

ca.  25  degrees 

0.47 

middle,     Ar  —  Xe 

12 

0.21 

Chloroids:       initial,      Fl—  Cl 

60 

1.73 

middle       Cl—  lo 

26         •*"  •  • 

0.49 

Sulph-Phosphoids  initial        N  —  P,  S 

83 

8.14 

middle  P,  S—  Sb, 

Te      70 

2.75 

terminal  Sb  —  Bi 

34 

0.67 

Kaloids  :                          Na  —  Ka 

41         " 

0.87 

Cadmoids  :       middle,    Zn  —  Hg 

41 

0.87 

For  the  phosphoids  and  sulphoids  we  have  taken  a  middle 
value,  the  two  lines  rising  almost  in  the  same  manner. 

The  following  are  the  most  notable  conclusions  that  may  be 
read  from  the  values  just  given.  It  will  be  borne  in  mind  that  the 
tangent  represents  the  rise  per  unit,  so  that  the  rise  per  hundred 
is  obtained  by  moving  the  decimal  point  two  places  to  the  right. 
For  the  middle  of  the  argonoids  the  diagram  shows  the  line  to  be 
inclined  under  12  degrees  to  the  horizontal ;  the  common  tables 
show  the  tangent  of  12  degrees  to  be  0.21 ;  consequently  the  boil- 


23 

ing  point  rises  21  degrees  per  hundred   units   increase   of   the 
atomic  weights  for  argon  to  xenon.* 

1.  The  boiling  point  rises  the  least  for  the  argonoids,  ivhich  are 
nullovalent  (valence  zero).  This  rise  is  only  47  degrees  per  hun- 
dred atomic  weight  for  the  initial  part,  and  less  than  half  that 
amount  (21)  for  the  middle  part.  2.  The  middle  line  of  the 
monovalent  chloroids  rises  as  much  as  the  initial  part  of  the  nul- 
lovalent argonoids  (about  48  degrees  per  hundred  increase  of 
atomic  weight).  3.  The  strange  fact  that  the  rise  for  sulphoids 
and  phosphoids  is  so  closely  alike  throughout  both  genera,  may 
be  connected  with  their  so-called  abnormal  vapor  densities  at 
the  boiling  point.  Troost^  considers  sulphur  vapors  at  this  point 
comparable  to  ozone  —  which  would  explain  the  equality  of  the 
rise  for  divalent  sulphur  to  that  of  trivalent  phosphorus.  We 
might  actually  repeat  the  words  which  Troost  (1.  c.)  uttered  a 
quarter  of  a  century  ago:  "This,  it  seems  to  me,  is  the 
"  closest  analogy  that  can  be  invoked  to  reconcile  facts  of  this 
"nature." 

Final  Conclusions. 

Passing  into  review  all  facts  and  general  relations  between  boil- 
ing and  fusing  points  on  the  one  hand  and  atomic  weights  on  the 
other,  we  must  draw  the  following  general  conclusions :  — 

Both  the  fusing  and  the  boiling  points  of  the  chemical  elements 
are  manifestly  dependent  upon  the  atomic  weight  of  the  same  ;  but 
that  relation,  while  strongly  marked,  is  not  expressive  by  the 
common  "  rule  of  three,"  nor  can  these  points  be  said  to  be  even 
increasing  with  the  atomic  weights,  for  the  very  sign  of  the  varia- 
tion changes,  being  positive  for  metalloids,  and  negative  for 
strongly  pronounced  electropositive  metals,  while  for  the  least 


*  While  reading  this  proof  we  obtained  the  fusing  points  of  the 
higher  Argonoids  from  the  Catalog  (British  Exhib.  Group  23)  and  have 
entered  them  on  our  large  original  drawing. 

The  fusing  point  line  practically  coincides  with  the  boiling  point  line 
at  argon,  and  forms  an  angle  of  about  4  degeees  below  the  latter. 

The  fusing  point  of  the  argonoid  triad  rises  therefore  only  11  degrees 
per  hundred  increase  of  atomic  weight. 

f  Comptes  Rendees,  T.  86,  p.  1396;   1878. 


24 

volatile  and  fusible  metals  the  entire  influence  of  atomic  weight 
is  relatively  small. 

While  the  direction  of  the  change  varies  with  the  electric 
character  of  the  element  it  appears  that  the  amount  of  the 
change,  for  pronounced  electropositive  or  electronegative  ele- 
ments is  approximately  equal  for  the  same  increase  in  atomic 
weight,  not  of  the  element  itself,  but  for  a  unit  of  valence  of  the 
same. 

Finally,  all  these  remarkable  relations  —  most  of  which  have  been 
brought  to  light  by  our  method  of  graphical  research  here  used  — 
make  it  impossible  to  look  upon  the  chemical  elements  as  un- 
related, independent  substances,  for  these  mathematical  relations 
(here  expressed  geometrically)  are  inconceivable  on  any  supposi- 
tion but  that  all  chemical  elements  are  compounds  of  groups  or 
links,  of  one  and  the  same  material  united  according  to  ap- 
parently very  simple  and  very  few  modes  of  combination. 

The  last  clause  of  our  conclusion  is  based  upon  the  facts 
above  established  that :  — 

First,  in  each  genus  of  elements  we  can  distinguish  a  front, 
middle  and  last  term,  the  middle  consisting  of  three  elements,  a 
triad. 

Second,  the  sign  of  increase  is  positive  for  electronegative  ele- 
ments, and  negative  for  pronounced  electropositive  elements, 
while  the  amount  is  roughly  the  same  for  both  per  unit  of  valence. 

Third,  for  elements  (metals)  of  no  pronounced  electric  charac- 
ter, the  change  is  neither  positive,  nor  negative,  but  quite 
insignificant  either  way. 

FUSING    POINT    AND    VALENCE. 

The  somewhat  detailed  exposition  of  the  relations  of  the  fusing 
point  of  the  chemical  elements  to  their  atomic  weight  has  shown 
that  the  valence  and  electrical  character  of  the  elements  are  really  de- 
termining the  character  and  amount  of  the  influence  of  the  atomic 
weight  itself.  It  may  therefore  be  advisable  to  consider  these 
most  fundamental  effects  of  valence  and  electrical  character  once 


25 

more  and,  as  it  were,  independent  of  the  atomic  weight  as  such. 
This  apparently  impossible  condition  we  can  readily  fulfill  by  con- 
sidering the  genera  as  such,  arranging  them  according  to  valence 
and  tension  (if  we  may  use  this  term  for  brevity's  sake).  This 
is  precisely  what  we  have  been  publishing  since  1867,  and  what 
constituted  the  basis  of  our  Natural  Classification  of  the  Chemi- 
cal Elements.  The  history  of  this  classification  is  given  in  our 
True  Atomic  Weights,  1894,  pp.  227-239. 

In  Plate  10  the  data  of  observation  have  been  graphically 
represented  in  our  usual  manner.  The  original  drawing  was 
made  on  half  a  sheet  of  double  elephant  drawing  paper,  the  tem- 
perature scale  used  being  100  degrees  to  the  inch  —  a  scale 
abundantly  large  when  a  range  of  temperature  of  two  thousand 
degrees  is  to  be  represented.  The  part  represented  on  our  plate 
reaches  from  the  absolute  zero  to  1950,  thus  extending  over  2120 
degrees  Centigrade  so  far  as  our  ordinate  is  concerned. 

The  genera  of  elements  have  been  placed  at  equal  distances 
apart,  and  arranged  in  accordance  with  tension  and  valence. 
Conform  to  the  exclusive  practice  of  modern  chemical  authors  we 
exceptionally  place  the  metalloids  first  in  this  plate  ;  we  use  this 
rather  irrational  order  to  put  the  subject  once  in  conformity  with 
modern  fashion. 

At  the  foot  of  the  plate,  all  necessary  data  as  to  tension  and 
valence  have  been  placed,  also  our  (Greek)  symbols  of  the 
genera  —  the  names  of  which  are  written  out  in  full  on  the  upper 
part  of  the  ordinates.  In  the  upper  left  hand  corner  we  have 
added,  for  convenience  of  readers  not  yet  familiar  with  our  Carbon 
System  of  the  Elements,  a  tabular  view  of  the  same  with  symbols 
and  atomic  weights.  We  have  also  in  this  table  arranged  the 
genera  beginning  with  the  metalloids,  to  make  this  table  conform 
to  the  plate. 

For  each  element,  the  fusing  point  has  been  marked  on  the 
ordinate  of  the  genus  to  which  it  belongs.  These  marks,  and  the 
lines  connecting  the  corresponding  elements  of  the  different  genera, 
have  been  marked  so  as  to  readily  distinguish  the  elements  in 
each  genus  according  to  their  order:  the  first  or  initial  element 
is  marked  by  a  small  black  circle,  and  these  circles  are  joined  by 
a  single  rather  light  line.  Tracing  this  line  we  start  with  Fl, 


26 

then  find  N,  both  near  the  line  of  absolute  zero ;  then  occurs  the 
discontinuity  —  probably  the  most  remarkable  in  nature  —  for  the 
fusing  point  of  carbon  lies  far  beyond  the  upper  limit  of  our  plate 
(certainly  above  3000  degrees)  and  is  only  indicated  by  the  arrow 
pointing  upwards  under  the  letter  C,  the  symbol  of  carbon.  The 
fusing  point  of  Bo  is  also  beyond  the  limit  of  our  plate ;  Be  and 
Li  are  represented  on  the  right  marginal  line  of  our  chart.  The 
using  point  of  hydrogen  has  been  added  in  the  left  margin  of  our 
chart. 

The  middle  part,  constituting  the  triad  of  each  genus,  has 
been  represented  so  that  it  can  most  readily  be  traced  throughout 
the  system ;  this  is  necessary  to  impress  the  radical  reverxinn 
exhibited  in  their  order  for  metals  and  metalloids,  which  developed 
in  our  study  of  this  subject  just  concluded. 

To  mark  most  strikingly  the  general  succession  of  the  genera 
we  have  marked  the  elements  of  the  middle  member  of  each  triad 
by  a  full  black  circle,  and  connected  these  for  the  genera  by  a 
single  heavy  line  —  which  should  be  traced  by  the  reader  as  fol- 
lows: Br,  Se,  As,  Ge,  Ga,  Zn,  Ka. 

The  first  member  of  each  triad  is  marked  by  an  open  r//v/r, 
which  is  connected  by  a  Hyht  sniffle  line  from  genus  to  genus. 
Trace:  Cl,  S,  P,  Si,  Al,  Mg,  Na  and  notice  the  great  discontinuity 
between  P  and  Si,  corresponding  to  the  almost  infinite  discon- 
tinuity between  N  and  C. 

The  third  or  last  member  of  each  triad  is  marked  by  an  open 
circle  of  larger  diameter  in  which  a  small  central  black  circle  is 
shown,  and  these  marks  are  joined  by  a  double  line.  The  reader 
is  requested  to  trace  the  third  member  through  the  genera,  as 
follows:  lo,  Te,  Sb,  Sn,  In,  Cd,  Rb.  It  will  be  noted  that  the 
discontinuity  Sb — Sn  is  relatively  small  and  reversed  in  direction, 
being  downward. 

Finally,  the  terminal  member  of  each  genus  has  been  marked 
by  a  large  black  circle,  and  these  are  joined  by  a  double  hear)/  fine. 
Trace:  Bi,  Pb,  Tl,  Hg,  Cs. 

The  mean  fusing  point  for  each  genus  is  marked  by  an  open 
circle  with  an  oblique  cross.  For  the  chloroids,  phosphoids  and 
kaloids,  all  data  are  observed.  For  the  sulphoids,  we  have 
taken  — 181  as  the  fusing  point  of  oxygen.  For  the  adaman- 


27 

toids  we  assumed  C  3000  and  Si  2000  ;  we  also  took  Bo  at  2000, 
and  Mg  at  900.  It  is  quite  evident  that  even  an  apparently 
large  error  in  these  numbers  will  not  affect  the  resulting  mean 
seriously. 

In  this  way  the  places  of  the  means  have  been  obtained,  as 
marked:  Chloroids, — 57;  Sulphoids,  150;  Phosphoids,  301; 
Adamantoids,  about  1300;  Styphoids,  about  640;  Cadmoids, 
about  520  and  kaloids  82  degrees  Centigrade. 

The  mean  fusing  point  of  a  genus  of  chemical  elements  increases 
with  the  numerical  value  of  its  valence.  It  is  highest  for  the 
tetravalent  adaman toids,  and  decreases  gradually  to  each  side 
thereof  as  the  valence  falls  from  four  to  one,  whether  the  elements 
be  metalloids  (to  the  left)  or  metals  (to  the  right)  of  the  adaman- 
toids. 

This  general  fact  we  have  insisted  on  since  1867  ;  it  applies 
also  to  the  boiling  points,  and  together  with  the  electrical  contrast 
has  formed  the  basis  of  our  natural  classification  of  the  chemical 
elements. 

Passing  next  to  the  examination  of  tke  different  genera  in 
detail,  it  will  be  noticed  that  the  two  genera  of  metalloids  are 
strictly  what  may  be  termed  normal  in  showing  a  gradual  rise  of 
their  fusing  point  with  the  increase  of  this  atomic  weight ;  the 
order  upwards  is  Fl — Cl — Br — lo  and  O — S — Se — Te. 

The  same  holds  good  for  the  first  four  of  the  phosphoids : 
N — P — As — Sb  ;  but  the  fifth,  Bi,  shows  a  most  marked  inver- 
sion, its  fusing  point  being  almost  midway  between  that  of 
phosphorus  and  arsenic,  while  its  atomic  weight  exceeds  that  of 
arsenic  by  133. 

For  the  adamantoids,  the  first  four  elements  show  this  same 
inversion,  while  the  fifth,  Pb,  shows  a  small  increase  over  the 
fourth,  Sn,  in  the  normal  direction.  Thus  the  order  of  fusibility 
of  the  adamantoids  is  entirely  reversed  a#  compared  to  that  of 
the  phosphoids,  even  in  the  minute  detail  marked  by  the  fifth 
member  of  these  genera. 

The  same  inversion  is  marked :  — 

first,  by  the  sudden  rise  from  near  the  absolute  zero  (N)  to 
about  three  thousand  degrees  above  (C)  ; 


28 

second,  by  the  steep  rise  of  almost  1400  degrees  from  P  to  Si ; 
third,  by  the  moderate  rise  of  about  50  degrees  from  As  to  Ge  ; 

fourth,  by  the  fall  of  about  40  degrees  from  Sb  to  Sn,  neces- 
sary to  completely  inverse  the  order  in  the  triads 

phosphoids  :     P  —As — Sb  upwards  ; 
adamantoids :  Si — Ge — Sn  downwards. 

Fifth,  as  already  stated,  the  fifth  members  are  inverted  in  these 
two  genera:  from  Sb  to  Bi  a  fall,  hence  from  Sn  to  Pb  a  rise. 

This  inverted  order  of  the  metalloids  now  remains  permanent 
for  the  rest  of  the  metallic  genera,  constituting  the  most  striking 
contrast  between  metals  and  metalloids. 

For  the  styptoids,  the  fifth  member  Tl  is  still  above  the  fourth 
In  as  Pb  over  Sn  in  the  adamantoids ;  but  in  the  cadmoids  and 
kaloids  the  entire  order  is  the  exact  inverse  of  that  of  the 
chloroids  and  sulphoids  of  the  metalloids. 

The  apparent  special  anomaly  of  the  fifth  member  is  thus 
restricted  to  the  highest  valencies  three  and  four,  characterizing 
the  genera  styphoids,  adamantoids  and  phosphoids. 

We  may  also  express  this  rather  complex  condition  of  things 
in  the  following  manner :  The  metals  of  lowest  valence  present 
the  metallic  character  the  most  completely  ;  so  do  the  metalloids 
of  the  lowest  valence  represent  the  non-metallic  character  the  best. 
This  is  also  indicated  by  their  electrical  contrast  or  potential 
tension  being  the  highest. 

Now,  neither  for  the  most  pronounced  metalloids,  nor  for  the 
most  pronounced  metals,  do  we  find  any  inversion  of  the  order 
for  the  fifth  member  of  a  genus.  For  these  metalloids  the  fusing 
point  increases  without  exception  as  the  atomic  weight  increases  ; 
in  the  same  way,  the  mono-  and  di-valent  metals  have  a  lower 
fusing  point  for  higher  atomic  weight,  without  exception. 

But  for  the  tri-  and  tetra-valent  metals,  this  order  is  inverted 
for  the  last  member  of  each  genus  ;  and  so  it  is,  in  the  same  way, 
for  the  last  member  of  the  tri-valent  phosphoid,  the  brittle  metal, 
bismuth. 

Our  diagram,    representing  the   fusing   point  as   function   of 


29 

valence  and  electrical  tension,  brings  out  this  fundamental  con- 
trast more  strongly  than  an}-  other  representation  presented. 

The  signification  of  this  contrast  a3  to  the  nature  or  constitu- 
tion of  the  chemical  elements  must  be  of  the  highest  value ;  we 
shall  soon  inquire  into  this  question. 

Before  doing  so  we  must  put  into  language  a  quantitative  rela- 
tion which  we  have  referred  to  repeatedly  as  we  recognized  it 
from  different  points  of  view,  and  which  presents  itself  in  this 
diagram  also  in  the  most  forcible  and  clearest  way. 

For  the  initial  member  of  the  seven  genera  of  elements  here 
considered,  the  total  range  in  fusing  point  is  the  greatest;  it 
exceeds  three  thousand  degrees  centigrade. 

For  the  second  member  (being  the  first  of  a  triad)  the  range  is 
reduced  to  only  about  one-half  of  the  above,  say  1,500  degrees. 

For  the  third  member  of  these  genera,  being  the  second  mem- 
ber of  the  corresponding  triads,  this  range  is  again  greatly 
reduced  to  but  little  above  half  of  the  just  preceding  range  ;  the 
difference  Gre — Br  being  less  than  900  degrees. 

For  the  fourth  member  of  these  genera,  or  the  third  member  of 
the  triads,  the  extreme  range  is  Sb — Rb  or  about  600  degrees. 

Finally,  for  the  fifth  member  we  have  no  observations  for  the 
chloroids  and  sulphoids,  no  fifth  member  yet  having  been  found  ; 
the  extreme  range  is  Pb — Hg  or  about  400  degrees. 

The  range  in  fusing  point  diminishes  roughly  in  a  geometrical 
proportion  with  the  arithmetical  increase  of  the  order  in  the 
genera.  The  second  is  half  of  the  first;  the  third  (900)  is 
greater  than  half  of  the  second  (750),  more  nearly  two-thirds 
( 1000).  Going  on  with  this  ratio  from  the  third  (900)  we  get  600 
which  is  the  fourth,  and  two  thirds  hereof  is  400  which  is  the 
fifth  as  observed. 

It  must  be  understood  that  no  exact  ratios  are  pretended  to 
have  been  found,  but  it  cannot  be  denied  that  the  range  decreases 
roughly  in  a  geometrical  ratio  as  the  order  in  the  genera  increases 
arithmetically  from  the  first  to  the  fifth. 

This  means  that  the  logarithm  of  the  temperature  range  approx- 
imately indicates  the  order  in  the  genus.  It  is  a  most  general 
relation  between  dependent  quantities  in  nature ;  but  it  is  not 
possible  here  to  enter  further  upon  this  question  of  detail. 


30 


CONCLUSION. 

It  is  impossible  to  observe  the  rapidly  diminishing  range  in  the 
fusing  points  of  these  chemical  elements  without  recognizing 
therein  a  mechanically  irresistible  argument  for  the  composite 
nature  of  the  chemical  elements. 

In  passing  from  the  first  to  the  fifth  and  last  known  member 
in  each  genus  of  elements,  the  general  chemical  and  physical 
characters  are  preserved,  but  the  contrast  expressed  in  the  range 
of  fusing  points  decreases  in  a  geometrical  ratio.  Thejirst  order 
of  members  differ  extremely  as  to  oxygen,  diamond  and  lithium ; 
the  fifth  order  of  members  closely  resemble  one  another,  for  they 
are  Bismuth,  Lead,  Thallium,  Mercury  and  Cesium. 

The  atomic  weights  of  the  different  members  of  one  order 
differ  only  about  ten  units  from  their  mean,  which  is  that  of  the 
corresponding  adamantoid.  Thus  Lithium  is  7,  Fluorine  19, 
which  is  respectively  5  below  and  7  above  carbon  12  in  thefirxt 
order.  In  the  fourth  order,  iodine  is  seven  above,  cadmium  is  6 
below  the  atomic  weight  118  of  the  adamantoid  tin.  The  kaloids 
in  brackets  cannot  here  be  compared,  as  we  soon  shall  learn. 

To  study  the  atomic  weight  of  these  orders,  we  therefore  can 
take  the  atomic  weight  of  the  adamantoids  as  type ;  for  the 
metals  are  but  little  below,  while  the  metalloids  are  but  little 
above  this  weight. 

The  following  series  represents  these  data  for  the  adamantoids : 

Symbol  C          Si          Ge          Sn  Pb 

Atomic  Weight  12         28  73          118         207 

Increase  16        45          45  89 

Now,  89  is  but  one  unit  short  of  90,  which  equals  the  increase 
from  Si  to  Sn.  Furthermore,  45  is  but  3  sjiort  of  48,  which  is  3 
times  16,  the  first  increase.  We  find  exactly  such  laws  of  com- 
bination in  organic  chemistry,  in  the  so-called  radicals ;  but  we 
shall  not  enter  upon  these  comparisons  here. 

We  shall  merely  take  notice  of  the  observed  fact,  that  the  atom 
of  silicon  contains  16  units  of  weight  more  than  the  atom  of 
carbon  ;  an  atom  of  germanium  contains  nearly  three  times  that 


31 

increase  more  than  silicon ;  that  an  atom  of  tin  again  contains 
exactly  this  amount  of  matter  more  than  germanium,  and  that  an 
atom  of  lead  contains  double  this  addition  of  matter  above  that 
of  the  atom  of  tin. 

In  other  words,  let  us  reason  about  matter  as  some  one  identical 
thing,  measured  by  weight  only,  but  not  otherwise  different. 

Then  the  atom  of  carbon  for  some  reason  is  chemically  quadri- 
valent. In  the  silicon  atom  we  have  this  same  carbon  atom 
(weight  12)  lengthened  by  exactly  16  units  of  weight  of  the  same 
matter,  constituting  the  atom  of  silicon,  which  has  the  same  chem- 
ical character  (quadrivalence,  etc.),  because  its  active  headisihe 
same  identical  matter  constituting  the  carbon  atom,  which  has 
somehow  picked  up  the  weight  16. 

The  silicon  atom  combining  with  three  such  particles  of  16  — 
which  to  permit  close  combination  have  each  lost  one  so  as  to 
leave  each  a  weight  of  15  only,  constitutes  the  germanium  atom. 

An  equal  increase  by  3  such  weights  of  15  each  gives  the 
weight  of  the  tin-atom,  always  supposing  that  the  original  weight 
12  continues  the  quadrivalent  head,  the  same  as  the  carbon  atom. 

Finally  adding  double  this  amount  of  matter  or  twice  45  less 
one  unit  to  permit  combination,  we  have  the  weight  of  the  lead 
atom. 

As  to  how  this  matter  is  joined,  there  are  many  possibilities. 
One  of  them,  apparently  the  most  simple,  would  be  to  suppose 
the  second  (16)  to  continue  in  line  with  the  first  (12),  making 
the  silicon  atom  to  consist  of  two  links.  If  the  other  matter  be 
added  all  in  the  same  direction,  the  atom  or  germanium  would 
consist,  first,  of  the  carbon-head,  weighing  12,  then  four  links, 
the  first  weighing  16,  the  next  three  weighing  15  each,  total 
length  5  links,  total  weight  73. 

The  next  45  as  three  links  would  make  the  atom  of  tin  consist 
of  8  links  weighing  118. 

Finally  6  more  links,  aggregating  89  units  (instead  of  the  6 
times  15  or  90)  would  make  the  atom  of  lead  consist  of  14  links 
weighing  207  units. 

Such  combinations  we  have  in  organic  chemistry.  The  com- 
pound methane  (marsh  gas)  has  the  atomic  weight  16,  consisting 


32 

of  one  carbon  12  and  four  hydrogen.  Being  saturated,  it  does 
not  directly  combine  ;  does  not  act  like  a  chemical  element. 

But  if  by  any  proper  chemical  treatment  one  atom  of  hydrogen 
be  removed,  the  residue  is  termed  the  chemical  radical  methyl;  its 
atomic  weight  is  15,  its  valence  is  one  (namely  the  place  vacated 
by  hydrogen).  This  radical  forms  compounds,  exactly  as  do 
the  monovalent  elements. 

The  next  organic  radical  is  ethyl;  it  is  also  monovalent,  its 
atomic  weight  is  29,  containing  two  links:  the  active  head  14, 
the  next  methyl  15. 

Then  follows  propyl  of  3  links,  butyl  of  4  links,  up  to  36 
links.  Each  of  these  radicals  has  the  same  monovalent  active 
head;  the  body  increases  14  in  weight  for  each  additional  link. 

These  are  organic  radicals  of 

1258  14       links 

Weigh,  15         29         71         113         197 

Increase,  14         42         42  84 

It  will  be  noticed  that  this  series  of  actually  well-known 
organic  radicals  is  astonishingly  parallel  to  the  above  given 
series  of  the  adamantoids. 

If  the  series  of  radicals  1,  2,  3,  8,  14  be  combined  with 
hydrogen,  we  get  the  corresponding  paraffins  so-called ;  if  with 
Fl,  Cl,  Br,  lo,  Cyanogen  (itself  a  monovalent  radical)  we  obtain 
the  corresponding  fluorides,  chlorides,  bromides,  iodides  and 
cyanides.  The  boiling  points  of  these  well-known  organic  com- 
pounds are  graphically  represented  on  Plate  5,  where  the  tem- 
perature is  laid  off  as  ordinates  or  vertically,  while  the  number  of 
links  is  represented  by  its  logarithm  as  abscissa. 

This  diagram  we  copy  from  its  first  publication  in  the  trans- 
actions, the  Comptes  Rendus  (T.  115,  p.  177)  of  the  Academy 
of  Sciences  of  Paris,  to  which  Berthelot  presented  my  paper 
(Note  No.  28)  on  this  subject,  July  18,  1902. 

Now,  in  this  paper  the  boiling  points  of  all  compounds  repre- 
sented on  this  plate  were  calculated  from  the  rectilinear  structure 
of  the  same ;  the  calculated  temperatures  were  found  to  agree 
with  the  temperatures  actually  observed. 


33 

The  compounds  here  specially  of  interest  are  those  correspond- 
ing to  the  above  specified  values  of  n,  the  number  of  links ;  that 
is,  the  numbers  1,  2,  5,  8  and  14. 

If  the  links  in  these  organic  compounds  were  not  all  in  one 
straight  line,  but  arranged  in  any  other  way  the  temperatures 
calculated  from  this  special  position  of  the  links  would  not  have 
agreed  with  the  actually  observed  boiling  points. 

The  agreement  or  disagreement  of  such  calculated  values  thus 
positively  determines  whether  certain  chemical  compounds  have 
their  constituent  carbon  links  in  a  straight  line  or  not. 

If  for  example,  the  arrangement  had  been  this  way 

3  6  9         12 

1  2  4  7         10         13 

5  8         11         14 

(where  the  numbers  represent  the  consecutive  links,  each  weigh- 
ing 14),  then  the  calculated  boiling  points  would  have  been  much 
lower  for  the  higher  compounds  cohtaining  5,  8  and  14  links. 
In  the  above  instance,  four  links  would  have  been  treble,  and 
the  total  length  of  the  atom  would  have  been  6  only  instead  of 
14  measured  as  before. 

Again,  it  is  possible  that  the  three  links  3,  4,  5  surrounded 
link  2,  that  next  6,  7,  8  also  crowded  in  between  these  forming  a 
hexagon  with  2  as  the  center.  Finally  the  last  six  links  9  to  14 
might  find  their  places  around  the  preceding  hexagon.  Thus  the 
total  atom  of  lead  would  only  have  a  length  of  2  links,  but  in  its 
second  contain  13  times  the  weight  of  16  (or  rather  15).  See 
Principles,  1874,  pp.  181-182. 

These  are  some  of  the  possibilities  between  which  a  decision 
has  to  be  made  as  to  which  is  the  true  or  at  least  the  most  probable 
arrangement  of  the  total  matter  of  an  atom  of  lead,  tin,  german- 
ium, silicon  as  they  are  built  up  from  an  atom  of  carbon  weighing 
12  by  the  material  brick  or  link  weighing  15. 

It  is  evident  that  by  methods  such  as  have  been  referred  to  in 
connection  with  the  introduction  of  Plate  5  these  questions  can 
be  definitely  disposed  of.  But  this  problem  of  mechanics  is  more 
difficult  than  the  one  referred  to,  because  the  distances  between 

3 


34 

the  constituent  particles  are  undoubtedly  much  smaller  than  the  dis- 
tances between  the  element  atoms  in  chemical  compounds  such  as 
treated  of  successfully  in  our  above  note  in  the  Comptes  Rendus . 
At  any  rate  we  cannot  in  this  introductive  study  enter  upon  this 
problem  for  which  the  necessary  preparation  would  constitute  a 
full  treatment  of  our  mechanics  of  the  three  states  of  aggrega- 
tion. 

A  very  important  point  must  be  considered  right  here  relating 
to  the  apparent  selection  of  the  numbers  I,  3,  5,  6  representing 
the  additions  made  to  the  first  or  initial  element  atom.  Namely 
we  found  the  additions  as  follows :  first  16  ;  then  3  times  16  ; 
again  3  times  16,  and  finally  6  times  16  —  or  a  small  amount 
less.  In  the  case  of  the  adamantoids  the  additions  were 

16,  3  times  15,  3  times  15,  6  times  15  less  one. 

This  certainly  represents  a  definite  mode  of  selection,  namely 
the  selection  of  the  factors  stated :  — 


By  comparing  the  series  of  atomic  weights  for  the  other 
genera,  the  same  multiples  will  be  found  in  every  case  but  that 
of  the  kaloids. 

Thus  for  the  Styptoids,  the  values  are :  — 


Symbol 

Bo 

Al 

Ga 

In 

Tl 

At.  Weight 

11 

27 

70 

114 

204 

Increase 

16 

43 

44 

90 

Ratio 

1 

3 

3 

6 

Here  the  three  last  increments  are  43,  44  and  twice  45. 
For  the  Cadmoids  we  have 

Symbol          Be         Mg  Zn  Cd  Hg 

At.  Weight      9  24  65.5         112  200 

Increase  15  41.5  46.5         88 

Where   the    first    is    one  low,  the    mean  of  the  next  two    is 
exactly  44  and  the  last  is  exactly  twice  this  number. 


35 

For  the  Phosphoids  we  find 

Symbol  N  P  As          Sb  Bi 

At.  Weight      14  31  75  120          208 

Increase  17  44  45  88 

where   P  is  one  high  (Mg  was  one  low)  and  the  increments  are 
44,  45  and  twice  44. 

For  the  Sulphoids,  the  numbers  are 

Symbol          O  S  Se  Te  ? 

At.  Weight     16  32  79  124  ? 

Increase  16  47  45 

The  mean  of  the  last  two  is  46  ;  twice  46  or  92    added  to  124 
would  give  216  for  the  unknown  fifth  member  of  this  genus. 
The  Chloroids  show 

Symbol  Fl  Cl  Br  lo  ? 

At.  Weight     19  35.5       80          127  ? 

Increase  16.5       44.5         47 

The  mean  of  the  last  two  is  again  very  nearly  46  and  would 
indicate  an  atomic  weight  of  about  219  for  the  fifth  member  of 
this  genus  still  unknown. 

In  all  these  cases  the  increments  are  very  nearly  in  the  ratio 


The  first  is  exactly  16  for  the  sulphoids,  adamantoids  and 
styptoids  ;  also  for  the  kaloids  not  yet  considered  in  detail.  For 
the  cadmoids  it  is  15  ;  the  chloroids  show  16.5  and  the  phos- 
phoids  17. 

The  treble  increase  of  the  next  intervals  amounts  to  an  aver- 
age of 

46     for  the    chloroids  and  sulphoids, 

45       "     "     adamantoids, 

44       "     "     phosphoids,  cadmoids, 

43.5    "     "     styptoids, 

and  the  last  increase  is  quite  closely  double  this  value. 


36 

We  understand  that  the  difference  between  these  numbers  and 
three  times  16  or  48  indicates  the  number  of  bonds  that  hold 
these  increments  to  one  another  around  the  nucleus  already 
formed  —  if  we  may  reason  from  known  facts  relating  to  organic 
radicals  and  from  the  structure  of  inorganic  compounds,  the 
so-called  ternaries.  Programme  1867,  p.  16  ;  Principles  1874, 
p.  181. 

Turning  finally  to  the  Kaloids  we  find 


Symbol         Li 

Na 

Ka 

Rb 

Cs 

At.  Weight    7 

23 

39 

86 

133 

Increase 

16 

16 

47 

47 

Ratio 

1 

1 

3 

3 

Here  we  evidently  have  one  more  single  link  added  to  the  first 
element  atom,  Lithium.  The  binding  is  the  least  firm,  the  treble 
link  lacking  only  one  in  the  uncombined  3  times  16  or  48. 

It  appears  therefore  that  Potassium  is  related  to  Sodium  ex- 
actly as  the  latter  is  related  to  Lithium  —  the  additions  being 
made  in  a  straight  line,  forming  a  prismatic  body.  Then  the 
increase  goes  on  by  the  treble  link  as  in  the  other  genera. 

A  sixth  member  must  therefore  be  supposed  to  exist  in  this 
genus  of  elements.  Its  atomic  weight  would  be  twice  47,  that  is 
94  in  excess  of  the  last  named,  cesium  133 ;  this  gives  227  for 
the  sixth  kaloid.  No  such  element  is  known  at  present.  But 
the  next  group  corresponding  to  the  kaloids  and  built  exactly  on 
the  same  plan  is  the  following :  - 


Symbol 

Be 

Mg 

Ca 

Sr 

Ba 

At.  Weight 

9 

24 

40 

88 

137 

Increase 

15 

16 

48 

49 

Ratio 

1 

1 

3 

3 

The  next  higher  member  of  this  genus  —  embracing  the  old 
triad  of  the  Calcoids,  Ca,  Sr,  Ba  —  would  be  say  twice  48  or  96 
above  137,  that  is  233.  It  would  have  to  prove  its  calcoid  char- 
acter by  the  insolubility  of  its  sulphate,  by  its  flame  coloration, 
spectrum,  and  the  like. 

Seven  years  ago  no  such  element  was  known ;  nor  is  it  quite 
certain  that  such  an  element  has  been  discovered  to-day,  for  it 


37 

has  not  yet  been  produced  in  the  free  state.  But  the  chloride, 
bromide,  and  sulphate  of  what  is  called  radium  accord  excellently 
with  this  supposed  sixth  member  of  the  genus  considered,  or  a 
fourth  member  of  the  calcoids.  The  atomic  weight  determina- 
tions made  are  stated  to  give  225  ;  but  this  may  be  low,  since  it 
is  admitted  that  the  compound  operated  upon  did  still  contain 
some  barium.  The  examination  of  the  spectrum  of  radium  has 
convinced  Runge  and  Precht  that  this  value  is  too  low ;  they  cal- 
culate 258  from  their  spectroscopic  measurements.* 

It  is  quite  generally  accepted  by  chemists  to-day,  that  this 
much  renowned  radium  is  a  chemical  element  and  forms  a  fourth 
member  to  the  calcoid-triad.  In  case  that  view  is  proved  true, 
it  will  no  doubt  also  follow  that  its  atomic  weight  is  nearer  the 
figure  233  we  find,  than  the  figure  225  determined  by  the  dis- 
coverers of  this  substance,  the  Curies,  of  Paris. 

Many  other  chemical  elements  are  related  to  these  two  groups, 
the  higher  kaloids  and  the  calcoids,  both  in  their  chemical  char- 
acter and  in  their  atomic  weights  ;  they  are  commonly  known  as 
the  metals  of  the  rare  earths.  Their  chemical  investigation  is 
exceedingly  difficult  and  will  require  very  much  work  to  produce 
satisfactory  results. 

We  may  now  finally  examine  the  atomic  weights  of  the  group 
of  elements  named  palladoids  and  placed  near  the  cuproids  when 
studying  the  fusing  points. 

Symbols         Co  Pa  Pt 

At.  Weights  59  106  194 

Increase  47  88 

Ratio  1  2 

For  the  cuproids  we  have 

Symbol  Cu         Ag  Au 

At.  Weight  63.5       108  197 

Increase                      44.5  89 

Ratio                              1  2 

These  groups  correspond  to  the  last  three  members  of  the  gen- 


Berlin,  Sitzungsberichte,  1904,  pp.  423-425. 


38 

era  of  five  elements  first  considered,  but  at  least  the  palladoids 
cannot  possibly  be  connected  in  any  way  with  elements  of  low 
atomic  weight.  They  must  be  looked  upon  as  forming  a  system 
of  elements  by  themselves. 

The  most  common  typical  metal  of  this  system  is  iron ,  and  we 
have  therefore  called  this  entire  division  the  iron  system  of  chemi- 
cal elements. 

We  may  now  graphically  represent  all  known  elements  in  one 
diagram  according  to  their  fusing  point  and  atomic  weights. 
See  Plate  6. 

We  place  the  most  electropositive  kaloids  at  the  top,  and  the 
most  electronegative  chloroids  at  the  bottom,  with  the  iron  N//.S- 
tem  in  the  middle. 

The  ordinate  in  each  of  the  three  great  groups  so  resulting  is 
the  valence,  running  from  1  to  4  (adamantoids)  and  down  again 
to  one. 

The  abscissa  represents  the  atomic  weight  observed,  the  groups 
related  to  carbon  and  silicon  are  necessarily  common  to  the 
Kaloid  Division  at  the  top  and  the  chloroid  division  at  the 
bottom. 

From  these  the  other  elements  may  be  supposed  to  have 
grown  out  under  the  two  methods  already  brought  to  light,  char- 
acterizing the  Kaloidal  or  electropositive  division  and  the 
chloroidal  or  electronegative  division. 

In  the  Kaloidal  Division  the  first  increase  of  16  is  repeated,  as 
in  the  Kaloids ;  then  follows  the  treble  interval  (48  or  less)  twice, 
and  finally  the  double-treble  (96  or  less).  The  metals  of  the  rare 
eartJis  constitute  the  bulk  of  this  division  of  the  elements. 

In  the  chloroidal  division  the  first  increase  of  16  is  not  repeated, 
but  immediately  followed  by  twice  the  treble  interval  and  closed 
by  once  the  double  treble.  The  most  common  elements,  all  metal- 
loids and  the  heavy  fusible  metals,  belong  to  this  division. 

The  densest  and  most  difficulty  fusible  metals,  forming  the  iron 
system,  are  placed  between  these  two  divisions,  comprising  the  least 
fusible  and  least  volatile  of  all  elements.  In  this  division  we  can 
detect  no  simple  and  constant  valence  rule ;  the  valence  is  rather 
indefinite,  variable.  As  to  the  electric  character,  we  notice  a  most 
remarkable  peculiarity  in  the  iron  system.  The  lower  atomic 


39 

weight  here  is  associated  with  a  pronounced  electronegative 
character  (Cr,  Mo,  Wo)  while  the  higher  atomic  weights  are  less 
so  and  therefore  relatively  electropositive. 

In  both  the  other  divisions,  namely  the  kaloidal  at  the  top 
and  the  chloroidal  at  the  bottom,  the  electropositive  character  is 
peculiar  to  the  elements  of  lower  atomic  weight. 

The  small  Greek  symbols  marked  at  the  beginning  of  the 
Kaloidal  Division  may  be  used  to  designate  the  first  two  or  three 
members  only  of  each  genus ;  the  corresponding  names  are,  by 
valence : 

l,lithoids;   2 ,  berylloids  ;   3,  boroids. 

From  valence  4  to  1  down,  the  same  symbols  (only  lower  case) 
being  used  as  before,  the  names  remains  the  same. 

It  will  be  recognized,  that  this  system  makes  the  existence  of 
elements  with  atomic  weights  ranging  about  182  extremely  im- 
probable in  the  kaloidal  system  or  in  any  other.  Only  two  ele- 
ments are  located  here,  namely,  Ytterbium  and  Tautalium. 
Very  careful  research  on  these  two  elements  is  urgently  called 
for  to  determine  whether  for  the  longer  core  the  additions  con- 
tinue without  a  break  in  multiples  of  the  treble  3  times  16. 

Now,  having  obtained  an  idea  of  the  probable  genesis  of  the 
chemical  elements  from  one  single  material  substance,  which  we 
have  called  pantogen  we  may,  for  a  moment,  revert  to  the  question 
we  started  with,  namely  the  decrease  of  the  range  of  the  fusing 
point  in  a  geometrical  ratio,  as  we  pass  from  the  first  to  the  last 
of  the  five  members  of  each  genus  of  elements. 

The  first  elements  of  the  genera,  consisting  of  but  one  mass  of 
pan-atoms,  running  in  weight  from  7  in  lithium  to  19  in  fluorine 
(the  weight  of  a  hydrogen  atom  being  taken  as  unit)  is  first 
lengthened  by  one  weight  of  16  in  the  chloroidal  division,  then 
by  treble  this  weight  twice  in  succession,  finally  by  as  much  again 
(a  double  treble). 

The  increments  or  additions  are 

1....3....3....6          times  16. 

The  total  additions  to  the  first  member  therefore  are  1,  4,  7, 
13,  times  16. 


40  x 

In  the  kaloidal  division  we  find  the  addition  of  16  to  the  orig- 
inal atom  repeated  a  second  time ;  that  is,  the  increments  are 

1  ....  1  ...  3  ....  3  ...  6, 
and  the  additions  made  to  the  first  therefore  are 
1,  2,  5,  8,  14  times  16. 

As  now  the  first  element  of  each  genus  averages  the  weight  of 
a  carbon  atom  or  12,  we  notice  that  the  additions  are  rapidly 
increasing  and  therefore  must  rapidly  blot  out  the  striking  phy- 
sical properties  of  the  Jirst  member  while  the  chemical  character 
remains  largely  unchanged,  residing  exclusively  in  the  active 
head  or  first  nucleus  of  the  atoms  of  each  genus. 

This  is  precisely  what  we  see  so  strikingly  represented  in  our 
diagram  Plate  70,  where  the  line  of  the  fifth  members  Bi — Pb — 
Tl — Hg — Cs  is  generalized  in  the  curve  of  alternating  larger  and 
smaller  black  circles  shows  the  general  trend :  from  the  atomicity 
zero  rising  gradually  with  the  valence  to  the  tetravalent  lead, 
and  as  gradually  descending  with  the  lowering  valence  to  the  zero 
on  the  right. 

This  curve,  which  resembles  the  familiar  probability  curve, 
represents  the  final  extinction  of  the  striking  physical  contrast 
between  the  metalloids  and  metals  of  the  first  order :  Fl — O — 
N — C — Bo — Be — Li,  by  rapidly  increasing  equal  masses.  The 
first  contrast  has  also  been  typically  represented  by  the  curve  of 
tangents. 

Origin  of  the  Ratio  1:3:3:  6. 

We  have  compared  the  chemical  elements  to  organic  radicals, 
and  found  quite  a  resemblance  between  them.  In  both  we 
recognize  the  chemically  active  head,  which  marks  its  valence ; 
and  in  both  we  have  a  more  or  less  considerable  body  not  posses- 
sing active  chemical  properties,  but  greatly  modifying  the  physi- 
cal properties  of  the  element  or  radical  and  of  their  compounds. 
This  comparison  will  now,  we  trust,  be  much  better  understood 
than  it  was  at  the  time  we  first  presented  the  same. 

But  we  also  now  can  more  thoroughly  appreciate  at  least  one 


41 

striking  difference  between  the  series  of  organic  radicals  and  the 
series  of  elements  which  contribute  a  genus. 

In  the  series  of  monovalent  organic  radicals  beginning  with 
methyl  and  increasing  in  its  body  by  the  link  weighing  14  we 
know  every  member  corresponding  to  every  natural  member  from 
1  to  over  30.  But  in  the  series  of  elements  comprising  the 
chloroids  we  meet  only  the  additions  corresponding  to  the  mem- 
bers 1,  3,  3  and  6  giving  the  totals  1,  4,  7,  13.  Or  if  we  prefer 
to  count  in  the  first  element  (here  fluorine)  the  aggregates  or 
totals  are  (approximately)  represented  by  the  series  of  numbers 
1,  2,  5,  8,  14.  In  this  series  are  missing  the  numbers  3,  4;  6, 
7;  9,  10,  11,  12,  13  or  nine  in  all.  Of  all  14  numbers,  only 
Jive  are  found,  while  nine  are  absent. 

At  first  sight,  this  appears  very  strange  ;  it  is  one  of  the  sim- 
plest and  most  primitive  cases  (in  time)  of  aggregation,  akin  to 
crystallization.  A  nucleus  —  the  atom  of  second  element  in  the 
chloroid  (or  third  element  in  the  Kaloid)  combining  with  more  of 
the  pantagen  groupings  (of  weight  16  or  a  little  less,  as  we  have 
found)  will  complete  an  equilateral  triangle  with  three,  then  fill 
the  space,  completely  forming  a  hexagon ;  and  if  to  grow  still 
further,  it  will  require  again  six  such  bodies. 

In  the  middle  of  the  right  side  of  Plate  10  we  have  shown  this 
by  construction,  assuming  that  these  weights  16  form  equal  cylin- 
drical bodies.  The  different  marking  of  the  centers  has  simply 
been  done  to  distinguish  the  order  of  combination. 

In  the  growth  of  the  element-atom  we  seem  to  see  first  that 
little  body  which  will  remain  the  chemical  head  for  the  entire 
genus,  fixing  the  valence  thereof;  f.  Ex.  Fluorine.  This  atom 
axially  continuing  to  grow  takes  up  the  link  16,  forming  the  atom 
of  chlorine.  Three  such  links  equally  joining  in  an  equilateral 
triangle  around  this  nucleus  form  the  atom  of  bromine.  Another 
step  completes  the  hexagon  of  the  iodine  atom.  The  final  form, 
having  another  six  such  links  constituting  an  outer  hexagon,  forms 
the  highest  chloroid  element,  not  yet  discovered  by  the  chemist. 

The  question  of  contact  between  these  portions  is  involved  in 
the  lack  of  the  full  16  of  these  links  ;  we  cannot  consider  that 
subject  at  this  point. 


42 


TWO    GREAT    THINKERS. 

On  the  whole  it  does  not  seem  to  us  that  the  Pythagoreans  and 
Plato  were  so  very  foolish  in  their  ideas  about  the  nature  of  things, 
holding  that  the  essence  of  matter  is  expressible  in  numbers  or 
geometrical  forms.  We  certainly  have  here  come  face  to  face 
with  one  of  the  most  fundamental  facts  of  nature  expressed  by 
the  form  of  the  equilateral  triangle  direct,  inverted  and  redupli- 
cated. If  in  this  brief  inductive  exposition  we  could  find 
room  for  the  consideration  of  the  crystal  form  of  the  elements 
and  their  compounds,  we  would  again  meet  this  same  geometrical 
form  —  and  once  more  find  reason  to  admire  the  profundity  of 
the  great  thinkers  of  old  —  Pythagoras  and  Plato. 

As  an  expression  of  our  admiration  for  these  great  investigators 
who  twenty-five  centuries  ago  have  so  deeply  looked  into  the 
things  which  have  fascinated  and  determined  our  incessant  labors 
for  half  a  century,  we  have  copied  (Plate  10,  under  title)  the 
inscription  over  the  entrance  to  the  school  of  Plato :  ' '  Let  no 
one  enter  here  who  does  not  know  geometry,"  and  have  also 
chemically  modified  the  old  symbol  of  the  two  symmetrical 
equilateral  triangles  —  which  will  readily  be  recognized  as  geo- 
metrically identical  with  the  transverse  structure  of  the  chemical 
element-atoms  shown  on  the  opposite  side  of  Plate  10. 

And  if,  with  Solomon,  we  "  look  upon  the  lilies  of  the  fields," 
we  find  this  same  symbol  constructed  in  wondrous  beauty  in  each 
flower  of  a  day;  if  we  dig  the  crystal  gem  from  the  depths 
below,  we  again  behold  the  same  symbol  in  the  adamantine  luster 
of  its  geometrically  exact  facets. 

And  if  perchance  we  should  stray  into  or  at  least  with  eyes 
open  should  pass  by  one  of  the  grand  structures  erected  in  the 
"  dark  ages  "  by  men  animated  by  faith  in  the  unseen  truths  of 
God's  World  —  we  again  would  behold  that  triune  symbol 
wrought  in  stones  to  let  the  light  of  heaven  into  the  temple. 

THE    SYSTEM    OF    ATOMIC    WEIGHTS. 

The  systematic  classification  of  the  chemical  elements  based 
upon  their  fusing  point  and  valence  is  of  so  fundamental  impor- 


43 

tance  that  we  ought  to  confirm  the  result  just  obtained  by 
another  method  of  induction,  if  possible. 

We  have  published  such  a  method  in  our  True  Atomic  Weights 
in  1894  ;  we  shall  repeat  the  outline  here,  using  the  same  diagrams 
(Plate  IV  and  V  of  that  work  here  reprinted,  Plates  7  and  8. 

We  suppose  the  atomic  weight  and  valence  of  each  element  to 
be  known ;  we  also  know  their  general  relation,  their  genera. 
Nothing  more. 

For  each  natural  group  or  genus  of  elements,  we  arrange  the 
individual  elements  in  the  order  of  their  atomic  weight.  The 
sulphoids  f.  Ex:  O,  S,  Se,  Te,  .  .  .  .  In  this  order  we  call  them 
the  first  (Oxygen),  second  (Sulphur),  third  (Selenicum),/o?rfi 
(Tellurian). 

With  these  data  at  hand  and  which  data  can  be  taken  from 
almost  any  modern  work  on  chemistry,  we  graphically  determine 
the  place  (point)  of  each  element  on  a  large  sheet  of  drawing 
paper,  using  the  order  number  of  the  element  as  abscissa,  and 
the  atomic  weight  as  ordinate ;  the  latter  we  count  downwards 
for  convenience. 

In  this  manner  the  points  on  Plate  7  have  been  accurately 
determined,  this  plate  being  a  reduction  by  photography  of  our 
large,  most  carefully  constructed  drawing.  The  chemical  sym- 
bols is  entered  near  each  point  for  the  identification  of  the 
elements  referred  to. 

We  notice  first,  that  the  kaloids  form  the  extreme  limit  above 
and  to  the  right,  while  the  chloroids  form  the  limit  below  and  to 
the  left.  All  the  other  elements  fall  between  these  two  extremes. 
The  upper  right  empty  field  we  might  mark :  electropositive  ;  the 
lower  left  field :  electronegative. 

Now,  in  connecting  the  date  representing  the  individual  ele- 
ments of  a  genus  by  straight  lines  we  find  first  no  intersections, 
no  tangle  of  lines,  but  a  system  of  practically  parallel  groups  of 
lines. 

This  geometrical  fact  proves  that  the  chemical  elements  are 
built  or  constructed  on  essentially  one  and  the  same  plan. 

We  next  discover  that  the  points  marking  the  middle  three 
elements  (the  old  triad)  of  every  genus  form  a  straight  line,  very 
nearly  or1  exactly  so.  See  Cl — Br— lo  of  the  chloroids,  Ka — 


44 

Rb — Cs  of  the  Kaloids.  It  will  be  recognized  that  these  lines 
Cl — lo,  Ka — Cs  and  all  the  others,  are  practically  parallel  to  the 
line  B — C  which  has  its  terminal  abscissae  at  2  and  4  while  its 
terminal  ordinates  are  32  and  128,  that  is  two  times  16  and 
eight  times  16.  The  rise  in  atomic  weight  corresponding  to  the 
double  interval  from  2  to  4  is  therefore  six  times  16,  or  amounts 
to  three  times  16  for  each  of  the  single  intervals  from  2  to  3  and 
from  3  to  4. 

The  initial  line  joining  the  first  two  elements  in  each  genus  is 
seen  to  be  practically  parallel  to  the  line  A — B  which  from  the 
order  zero  to  two  falls  32  divisions,  or  has  a  fall  of  16  per 
order  unit.  Compare  lines  Fl — Cl  and  Li — Na,  the  extremes, 
and  notice  their  parallelism  with  line  A — B. 

The  final  lines,  joining  the  last  member  of  the  triad  with  the 
last  member  of  any  genus  (see  Sn — Pb)  is  practically  parallel  to 
the  line  C — D  which  in  one  interval  of  order  (4  to  5)  sinks  from 
C  at  128  to  D  at  224,  a  distance  of  96,  which  is  6  times  16. 

In  the  plate  only  six  genera-lines  have  been  drawn  out,  they 
are  seen  to  be  parallel  to  the  broken  line  A  B  C  D  just  character- 
ized. 

Accordingly  this  diagram  proves  geometrically  or  graphically 
that  in  every  genus  of  elements,  the  atomic  weight  rises  in  the 
initiatory  part  once  16  units  for  each  order  number,  in  the 
middle  or  triad-part  three  times  16  untits  for  each  order  num- 
ber, while  in  the  terminal  part  it  rises  six  times  16  units  for  each 
order  number. 

Here  we  have  graphically  (or  geometrically)  demonstrated  the 
great  general  fact  that  in  every  genus  of  chemical  elements,  the 
consecutive  individual  elements  result  from  the  first  by  an  increase 
in  atomic  weight  of  1:3:3:6  times  the  number  16,  as  near  as 
the  eye  can  detect  on  even  a  large  scale  drawing. 

In  order  more  readily  to  keep  track  of  the  elements  in  each 
order  number,  the  points  are  alternately  marked  by  open  (valence 
an  odd  number)  zndfull  black  circles  (valence  an  even  number). 
This  permits  the  more  ready  identification  of  the  elements  on  this 
chart. 

We  next  see  that  there  are  three  distinct  groups  of  chemical 
elements,  namely :  — 


45 

I.  Kaloidal  elements,  in  which  each  genus  has   two  elements 
built  up  by  the  addition  of  once  16  thus  forming  an  initial  triad, 
as  Li — Na — Ka,  marked  or  characterized  by  three  points  (three 
elements),  forming  but  one  straight  line  ; 

II.  Chloroidal  elements,  in  which  each  genus  has  but  one  ele- 
ment built  up  by  the  addition  of  once  16  ;  see  the  line  of  chlo- 
roids,  not  continuing  a  straight  line  from  Fl  to  Br,  but  only  to 
Cl;   and 

III.  The  ferroid  elements  which  do  not  start  (are  not  connected 
with)  the  initial  elements  under  A  B,  but  Jill   the  space  between 
the  two  preceding  groups  on  exactly  the  same  plan,  namely  devel- 
oping elements  parallel  to  the   lines  BC  and  CD  (triad  and  ter- 
minal).    Trace  the  line  of  sideroids:  Fe — Ru — Ir,  and  its  light 
(kaloidal)  branch  Sa — Ur. 

A  fourth  division  is  indicated  as  possible,  starting  about  172  ; 
but  thus  far  there  seems  to  be  no  indication  of  the  actual  exist- 
ence of  such  elements. 

If  we  now  wish  to  present  a  view  of  the  entire  system  of 
chemical  elements,  by  continuous  straight  lines  (unfolding 
A — B — C — D)  we  must  place  the  kaloidftl  elements  first,  the 
ferroidal  next  and  the  chloroidal  elements  last,  as  we  have  done 
in  our  Plate  6. 

If  we  wish  to  show  the  mode  of  accretion  or  growth  of  the  mem- 
bers of  the  several  genera  of  elements  in  the  plainest  and  simplest 
manner,  we  must  restrict  ourselves  to  the  representation  of  a 
typical  case  for  each  of  these  three  great  divisions  of  the  chemical 
elements. 

As  such  typical  cases  we  take  the  central  members  of  each 
division,  shown  on  our  Plate  8,  where  the  carbon  and  iron  sys- 
tems are  represented  in  outline. 

The  initiary  triad  C — Si — Ti  shows  a  visible  deviation  in  the 
last  member.  The  kaloidal  or  light  branch  is  Ti — Zr — Ce,  while 
the  chloroidal  or  heavy  branch  is  the  triad  Si — G-e — Sn  and  the 
terminal  Pb.  The  members  of  the  iron  group  have  just  been 
specified  above. 

As  a  matter  of  fact,  we  shall  soon  learn  that  the  kaloidal  branch 
is  made  up  of  elements  of  less  specific  gravity  than  the  chloroidal 


46 

branch.  We  therefore  conveniently  may  distinguish  these 
branches  by  the  simple  words  of  light  and  heavy  marked  on  Plate 
8  to  the  left,  where  the  mere  increase  in  the  three  great  divisions 
of  elements  is  shown,  starting  with  carbon  and  with  iron. 

No  initiary  gives  the  iron  group  ;  one  initiary  element  gives  the 
heavy  branch  of  the  carbon  system ;  while  two  initiary  elements 
lead  to  the  light  branch  of  the  carbon  system. 

We  may  also  call  attention  to  the  cross-section  marks :  3,  6 
and  12  circles  around  the  central  circle  representing  the  first 
member  of  the  triad. 

The  diagrams  in  the  upper  right  hand  of  this  chart  cannot  be 
considered  in  this  inductive  exposition. 

It  is  hoped  that  all  readers  are  sufficiently  familiar  with  graphic 
representations  of  numerical  relations,  that  is  geometric  reasoning, 
to  have  obtained  from  these  two  plates  a  clearer  insight  in  the 
constitution  of  the  chemical  elements  that  is  thus  geometrically 
and  therefore  mathematically  demonstrated. 

The  same  unity  or  plan  or  structure  was  obtained  in  the  pre- 
ceding section,  but  less  directly,  from  the  study  of  the  fusing 
points  in  connection  with  the  atomic  weights. 

In  concluding  this  topic  it  may  be  advisable  to  refer  to  one 
special  point  about  which  a  misunderstanding  may  creep  in  and 
do  considerable  harm.  I  refer  to  the  differences  between  the 
apparently  required  theoretical  value  and  the  value  furnished  by 
experience,  or  experiment. 

Now,  as  to  the  first,  it  must  be  understood  that  a  full  develop- 
ment of  a  theoretical  principle  often  shows  secondary  minor  vari- 
ations the  cause  of  which  at  first  remains  hidden.  Thus,  in  the 
majority  of  cases,  the  first  increase  of  atomic  weight  is  16  exactly. 
Yet  for  Mg  it  is  15  only,  and  for  P  it  is  17.  In  these  cases  evi- 
dently Be  is  too  high  (9)  making  the  interval  one  low,  while  for 
P  the  atomic  weight  is  one  high,  making  the  interval  also  one 
high.  The  real  question  here  is:  why  is  Be  9  instead  of  8,  and 
why  is  P  31  instead  of  30. 

The  first  of  these  questions  is  readily  answered,  for  a  general 
rule  is  plainly  visible  covering  this  case.  While  we  cannot  enter 
upon  details  here,  the  thoughtful  reader  will  notice  that  we  find 
a  regular  rise  by  two  from  carbon  to  oxygen  (three  elements) 


47 

broken  at  Fl  which  last  negative  is  one  high.  From  the  first 
positive  Li  we  find  a  regular,  constant  interval  of  two  for  three 
consecutive  elements  ;  this  makes  the  interval  Bo — C  only  one . 
Thus,  there  is  perfect  order  even  in  the  apparent  discrepancy ;  it 
could  be  mathematically  expressed  by  a  term  of  one  dependent 
on  the  valence. 

This  hint  may  be  sufficient  at  this  time. 

Again  it  must  also  be  borne  in  mind  that  the  numerical  data 
furnished  by  experiment  or  observation  are  not  necessarily 
exact,  but  may  be  in  error  themselves. 

The  main  thing  to  be  considered  in  this  connection  is  the  fact 
that  the  theoretical  requirements  as  now  understood  and  as  here 
represented  throughout  the  entire  field  of  the  better  known  chemical 
elements  agree  very  closely  with  the  data  now  known  as  the  result 
of  experimental  determinations  of  atomic  weights,  boiling  points, 
fusing  points,  specific  gravity  and  the  valence  and  electrical  char- 
acter of  the  elements. 

The  total   number  of  Chemical  Elements 

and  the  Cosmochemical  Flower. 

It  may  be  of  interest  to  try  to  answer  the  question :  how  many 
chemical  elements  exist  or  are  possible  according  to  our  system. 

The  general  view  of  our  system  shows  that  the  general  struc- 
ture is  the  same  for  each  valence.  There  must  then  be  eight 
such  systems  as  are  represented  for  the  valence  four  on  plate  8. 

We  distinguish  two  systems,  that  of  carbon  and  of  iron.  For 
the  first  we  have  the  initial  triad  or  3  elements  (C,  Si,  Ti)  with 
the  two  branches  ;  the  heavy  starting  from  Si  and  comprising  the 
triad  Si — Ge — Sn  and  the  terminal  Pb  ;  and  the  light  branch 
starting  from  Ti,  comprising  the  triad  Ti — Zr — Ce  and  also  (now 
admitted)  a  terminal  of  the  order  radium  and  thorium. 

Thus  we  recognize  the  existence  of  nine  distinct  chemical  ele- 
ments in  the  carbon  system  for  every  valence. 

This  makes  nine  times  eight  or  72  chemical  elements,  to  which 
must  be  added  the  internal  H  and  He  giving  74  elements  belong- 
ing to  the  complete  carbon  system. 

In  the  iron  system  the  valence  is  not  fixed,  but  we  know  repre- 


48 

sentatives  for  at  least  six  of  the  eight  valence  groups.  For  some 
of  these  we  know  the  entire  number  represented  on  plate  8, 
namely  the  triad  with  one  terminal  to  each  of  the  last,  also  dis- 
tinguished as  light  and  heavy  laterals.  This  makes  Jive  elements 
for  each  valence  or  forty  in  all. 

Accordingly  we  must  say  that  the  entire  number  of  chemical 
elements  that  have  formed  from  the  one  primary  matter  pantogen 
amounts  to  114. 

The  total  number  of  chemical  elements  actually  known  to-day  is 
not  more  than  tioo  thirds  of  this  number.  Surely,  the  young 
chemist  of  to-day  need  not  fear  that  the  field  of  work  is  ex- 
hausted and  that  there  remains  nothing  for  him  to  do. 

We  must  remember  that  we  have  pointed  out  the  possible  ex- 
istence of  a  still  higher  system  than  our  iron  system.  How  com- 
plex that  system  may  possibly  be  we  dare  not  dream  of ;  we  have 
enough  work  to  do  searching  for  the  host  of  elements  indicated. 

Having  obtained  an  estimate  of  the  total  number  of  chemical 
elements  we  would  like  to  see  them  all  equally  well  represented 
to  the  eye,  each  one  standing  out  as  plainly  as  any  other  element. 

Such  is  not  the  case  in  the  graphic  representations  of  the  chemi- 
cal elements  thus  far  used.  In  all  our  previous  diagrams  the 
dimensions  have  been  relatively  narrow  so  far  as  the  valence  is 
concerned,  crowding  the  element-genera  closely  into  parallel  lines. 
Only  the  diagram  Plate  10  is  free  from  this  objection,  showing 
the  genera  equally  well  as  to  valence,  but  it  covers  the  heavy 
members  of  the  carbon  system  only. 

In  Plate  11  we  have  produced  such  a  view  of  the  entire  system 
of  chemical  elements,  showing  all  groups  and  divisions  equally 
well. 

The  center  point  represents  pantogen,  the  prime  matter  from 
which  all  elements  are  supposed  to  have  been  formed.  From  that 
point  grow  out  eight  leave-like  systems  of  points,  all  alike,  and 
each  one  representing  one  valence :  the  lowest  zero,  upwards  ;  the 
highest  four,  downwards,  and  therefore  representing  the  nullo- 
valent  Argonoids  upwards,  the  quadrivalent  Adamantoids  down- 
wards. 

Between  these  two  vertical  leaves  we  see  both  to  the  right 
(electropositive)  and  to  the  left  (electronegative)  three  leaves 


49 

representing  elements  of  valence  one,  two,  three  in  numerical 
order. 

Thus,  the  full  blown  World-Flower  shows  the  following  eight 
leaves:  Upwards,  the  nullovalent  Argonoids;  to  the  right  the 
electropositive  elements,  first  the  monovalent  Kaloids,  next  the 
divalent  Cadmoids,  third,  the  trivalent  Styptoids.  The  next 
leaf,  directed  downwards,  represents  the  quadrivalent  Adaman- 
toids,  introducing  the  electronegative  elements  to  the  left :  first, 
the  trivalent  phosphoids,  next  the  divalent  sulphoids,  then  the 
monovalent  chloroids  which  again  are  succeeded  by  the  nullovalent 
Argonoids. 

It  is  not  necessary  to  dwell  upon  the  orderly  succession  of 
physical  properties,  such  as  fusing  point  and  the  like  ;  the  reader 
will  readily  recognize  the  completeness  of  this  graphic  represen- 
tation. 

Each  single  leaf  consists  of  two  distinct  parts  —  the  carbon 
system  and  its  iron  system  of  this  group.  In  a  more  complete 
representation  in  space  we  might  represent  it  by  two  leaves,  as 
every  flower  consists  of  a  calix  and  a  corolla ;  the  latter  would 
naturally  represent  the  higher  and  more  volatile  elements  of  the 
carbon  system,  while  the  former  would  call  to  mind  the  iron 
system. 

In  each  of  these  the  main  line  of  heavy  elements  is  marked  by 
the  full  black  circles,  while  the  open  circles  represent  the  corre- 
lated light  branch  of  elements.  In  the  latter,  the  radium  (or 
thorium)  link  has  not  been  drawn  ;  it  would  reach  out  the  furthest, 
for  the  circles  representing  the  elements  are  drawn  at  distances 
from  the  center  (pantogen)  proportional  to  their  atomic  weights 

In  order  not  to  diminish  the  main  graphic  value  of  this  sym- 
bolic and  yet  strictly  geometrical  diagram  drawn  to  scale,  we 
have  written  only  the  chemical  symbol  of  the  most  common 
(second)  member  in  the  carbon  system,  and  of  the  most  familiar 
first  member  of  the  iron  system.  By  means  of  the  details  given 
before,  any  reader  will  readily  identify  the  place  of  every  known 
element  at  the  proper  point  in  this  diagram.  He  will  then  also  find 
the  numerous  elements  which  we  cannot  doubt  do  exist,  but 
which  have  not  yet  been  discovered.  — See  the  corresponding 
statement,  p.  5,  close  of  paragraph  2  of  our  Programme  of  1867. 

4 


50 

If  we  were  inclined  to  make  a  show  of  profound  wisdom  at  a 
very  small  outlay  of  work,  we  might  enlarge  upon  the  properties 
of  these  unknown  elements.  A  mere  nothing  as  compared  to 
this  has  made  a  very  ordinary  chemist  most  famous,  and  then  he 
merely  hastily  generalized  what  he  had  read  and  seen  represented 
in  my  Programme  der  Atommechanik,  published  1867.  See,  also, 
True  Atomic  Weights,  1894,  pp.  239-255. 

As  the  construction  of  this  symbolic  flower  of  the  chemical 
elements  shows,  the  atomic  weight  increases  from  right  to  left,  in 
each  spire,  facing  the  flower,  so  far  as  the  carbon  system  or  the 
corolla  is  concerned. 

Since  the  calix  representing  the  iron  system  shows  the  same 
electrical  character,  the  atomic  weights  therein  diminish  from  right 
to  left. 

This  most  remarkable  feature  was  not  only  represented  but 
accentuated  in  the  corresponding  diagram  of  our  Programme  of 
1867,  which  diagram  has  been  reproduced  on  p.  215  of  our  True 
Atomic  Weights  in  1894,  and  on  page  396  of  our  General  Chem- 
istry in  1897,  where  on  p.  397  ihecosmochemical  flower,  Plate  11, 
was  first  published. 

By  spending  a  few  hours  study  on  this  flower  diagram,  using  all 
the  data  of  the  preceding  parts  of  this  little  introduction  to 
theoretical  chemistry,  many  known  relations  of  the  elements  will 
appear  in  a  clearer  light  and  many  new  relations  will  spring  into 
view. 

FREQUENCY    IN    DISTRIBUTION    OF    THE    ELEMENTS. 

This  may  also  be  the  best  place  to  consider  the  interesting 
question  of  the  frequency  or  relative  amount  of  the  different 
chemical  elements  and  their  distribution  or  location  in  nature. 

As  to  frequency  it  is  evident,  that  an  element  atom  will  form  so 
much  the  more  frequently  as  it  is  simpler  in  structure,  as  it  re- 
quires a  less  number  of  conditions  to  permit  its  formation. 
Therefore  we  must  hold  that  in  every  genus  the  frequency  is 
greatest  for  the  lowest  orders. 

By  the  same  rule  we  must  hold  that  the  light  elements  of  the 
carbon  system  must  be  less  frequent  than  the  heavy  elements. 


51 

This  has  long  been  recognized  in  the  common  term  of  the  rare 
earths  as  contrasting  with  the  ordinary  ones  of  the  heavy  branch. 

Thus  all  the  members  of  the  iron  system  may  also  be  consid- 
ered less  numerous  than  those  of  the  carbon  system. 

But  since  the  relatively  greater  frequence  of  the  atoms  of  the 
less  complex  elements  in  weight  is  possibly  fully  compensated  for 
by  the  individually  greater  weight  of  the  more  complex  atoms, 
there  may  in  all  nature  not  be  any  marked  difference  in  the  total 
weight  of  the  various  chemical  elements.* 

In  a  cosmical  sense,  a  given  weight  of  gold  may  be  as  common 
as  an  equal  weight  of  iron,  and  a  given  weight  of  silver  may  be 
as  common  as  an  equal  weight  of  tin. 

At  the  same  time,  there  must  necessarily  obtain  a  great  vari- 
ation in  the  frequency  of  the  chemical  elements  at  any  given  place 
in  the  world.  To  man,  living  on  the  surface  of  this  terraqueous 
globe,  gold  is  rare,  iron  is  common,  and  silicon,  magnesium, 
aluminum,  and  iron  form  the  bulk  of  the  rocks  of  the  outer  crust 
of  the  earth. 

Supposing  the  total  weight  of  the  different  elements  to  be  not 
very  different  in  the  world,  it  is  readily  understood  that  during 
the  countless  ages  that  have  elapsed  since  the  elements  formed 
from  the  prime-matter  (pantagent)  they  have  responded  to  all 
natural  agencies  in  virtue  of  their  individual  properties. 

Hence  to-day  the  lightest  elements  prevail  in  the  outermost 
parts  of  the  earth  and  other  commercial  bodies,  especially  in 
their  atmospheres.  Even  in  our  own  atmosphere  we  have  shownf 
such  a  partial  separation :  the  lower  strata  only  contain  the 
oxygen  and  nitrogen  ;  higher  up  first  the  oxygen  disappears  while 
hydrogen  becomes  more  frequent,  leading  to  an  outermost 
envelope  of  hydrogen  and  helium. 

The  gradual  change  of  the  main  rocks  of  the  outer  crust  of  the 
earth  has  been  studied  much,  also  in  comparison  with  the  two 
classes  of  meteorites,  stones  and  irons,  which  are  properly  con- 
sidered fragments  of  extra  terrestial  bodies.  This  question  has 


*  The  exact  relation  here  involved  has  been  studied  by  me  many 
years  ago,  also  in  reference  to  meteorites;  a  special  publication  hereon 
will  soon  be  issued. 

t  Comptes  Rendus,  1900,  August. 


52 

engaged  my  attention  frequently,  and  results  obtained  have  been 
stated  in  connection  with  my  earlier  publications  on  meteorites. 
As  I  am  now  ready  for  a  special  publication  on  this  subject,  this 
mere  mention  may  suffice  in  this  place. 

But  it  is  not  only  the  testimony  of  the  rocks  and  veins  acces- 
sible to  us,  nor  the  parallel  evidence  of  the  meteorites  that  is  at 
our  disposal ;  we  possess  most  absolute  astronomical  knowledge 
of  the  density  of  the  interior  part  of  the  earth,  according  to  which 
the  central  portions  of  the  earth  must  possess  a  specific  gravity 
of  at  least  16,  while  the  mean  density  of  the  earth  is  only  about 
5  and  the  outer  rocky  crust  only  about  two  and  a  half.  See 
publications  Planaof  1853. 

It  is  easy  to  demonstrate  from  these  data,  and  from  the  known 
density  of  the  elements  and  their  compounds,  that  the  central 
core  of  the  earth  must  consist  of  the  heaviest  of  the  knovm  elements 
as  such  or  in  the  state  of  alloys. 

It  is  not  even  the  fourth  member  —  from  silver  to  tin  —  but 
the  fifth  member,  from  gold  to  mercury,  that  can  furnish  the  only 
known  elements  to  bring  about  an  average  density  of  at  least  six- 
teen for  the  inner  core  of  our  globe. 

While  near  the  surface,  gold  is  rare,  in  the  depths  of  this 
globe  gold  and  the  like  elements  become  gradually  more  abun- 
dant, indubitably  forming  the  main  part  of  the  innermost  core 
of  this  earth. 

The  "  statistical  data"  furnished  from  certain  scientific 
bureaux  (where  a  lot  of  "  scientists  '  are  to  be  kept  mechanically 
doing  something  easy)  obtained  by  collating  actual  analyses  of 
rocks  and  minerals  made  by  the  hundred  in  other  divisions  of  the 
same  bureaux,  cannot  teach  anything  whatever  as  to  the  relative 
frequence  of  the  chemical  elements. 

The  Atomic  Volume  of  the  Elements. 

We  have  now  completed  a  simple  demonstration  of  the  compo- 
site nature  of  the  chemical  elements,  so  far  as  it  is  possible  in  a 
popular  form. 

It  has  been  shown  that  the  most  important  physical  properties 
of  the  different  elements  indicate  the  definite  structure  of  these 
elements  described  at  some  length. 


53 

For  detail  we  have  in  a  general  way  referred  to  our  publications 
on  this  great  subject,  enumerated  at  the  opening  of  this  work. 
We  have  not  made  many  specific  references,  because  that  would 
be  of  no  value  to  the  general  reader,  while  the  scientist  will  have 
to  make  himself  familiar  with  as  many  of  these  publications  as 
possible. 

It  has  been  specially  stated  that  our  publications  on  the 
mechanics  of  the  three  states  of  aggregation  are  of  special  impor- 
tance ;  a  new,  more  complete  work  on  this  topic  has  been  in  prep- 
aration for  a  number  of  years,  and  will,  it  is  hoped,  be  published 
within  a  year  from  this  time  —  in  which  case  it  will  have  been 
under  our  hands  for  exactly  half  a  century.  The  almost  forty 
Notes  published  in  the  Comptes  Rendus  treat  mainly  of  this  sub- 
ject, and  form  a  volume  of  140  pages  quarto. 

Supposing  now,  that  what  has  been  shown  here  as  to  the 
structure  of  the  atoms  of  the  chemical  elements  is,  in  the  main, 
conclusive,  it  would  be  very  desirable  to  confirm  these  results  by 
another  method  of  demonstration,  dependent  upon  another  funda- 
mental property  than  the  fusing  point  mainly  used  thus  far. 

Such  a  property  we  have  in  the  atomic  volume  of  the  chemical 
elements,  which  expresses  the  relation  of  the  atomic  weight  to  the 
specific  gravity  of  the  elements. 

It  will  be  remembered  that  we  temporarily  discontinued  the 
consideration  of  the  specific  gravity  of  the  elements,  replacing 
that  physical  property  by  the  chemical  determination  of  the  atomic 
weight. 

Having  now  studied  the  relations  of  fusing  and  boiling  point  to 
the  atomic  weight,  we  may  also  consider  the  precise  relations  of 
the  specific  gravity  to  the  atomic  weight. 

We  shall,  in  the  course  of  this  new  study,  find  a  most  con- 
clusive confirmation  of  the  results  obtained  by  the  study  of  the 
fusing  point. 

The  specific  gravity,  G-,  divided  into  the  atomic  weight,  a,  gives 
as  quotient  the  so-called  atomic  volume,  V ;  for  G  being  the 
weight  in  grammes  of  one  cubic  centimeter  of  the  element,  the 
quotient  V  evidently  represents  the  number  of  cubic  centimeters 
of  space  occupied  by  a-grammes  of  the  element,  that  is,  by  as 
many  grammes  as  the  number  a  indicates. 


54 

For  example,  the  atomic  weight  of  the  compound  water  is  18  ; 
its  specific  gravity  is  1 ;  the  quotient  V  is  therefore  18,  and 
indicates  that  one  gramme-atom  of  water  (18  grammes)  occu- 
pies a  volume  of  18  cubic  centimeters ;  that  is,  the  atomic  volume 
of  water  is  18. 

Again,  the  specific  gravity  of  liquid  hydrogen  (at  its  boiling 
point)  is  0.07 ;  its  atomic  weight  is  unity,  1 ;  hence  its  atomic 
volume  is  14.3,  which  means  that  one  gramme  of  liquid  hydrogen 
fills  a  space  equal  to  14.3  cubic  centimeters. 

Or  still  another  important  case:  the  specific  gravity  of  the 
diamond  is  3.50  to  3.55 ;  its  atomic  weight  is  12  ;  hence  its 
atomic  volume  is  3.43  to  3.38,  which  we  put  down  as  3.4,  and 
means  that  12  grammes  of  diamond  occupy  exactly  3.4  cubic 
centimeters. 

One  more  example  may  be  desirable  to  obtain  a  clear  insight 
into  the  determination  and  significance  of  the  atomic  volume.  The 
specific  gravity  of  metallic  potassium  has  been  found  to  be  0.865 
at  15  degrees ;  its  atomic  weight  is  39  ;  hence  its  atomic  volume 
is  45.1.  This  expresses  the  fact  that  39  grammes  of  potassium 
(Kalium)  occupy  45.1  cubic  centimeters  of  space. 

We  trust  it  is  now  fully  understood  what  is  meant  by  the  num- 
ber expressing  the  atomic  volume  of  any  chemical  compound  or 
element.  It  is  also  apparent  that  it  expresses  the  experimentally 
determined  specific  gravity  in  relation  to  the  equally  as  well 
determined  experimental  fact  of  the  atomic  weight  of  the  same 
compound  or  element,  so  that  we  have  in  the  atomic  volume  a 
numerical  quantity  determined  empirically  by  physical  and  chem- 
ical experiments  combined. 

We  may  therefore  examine  this  empirical  atomic  volume  and 
study  its  relations  to  any  other  experimentally  ascertained  fact ; 
as  such  we  will  here  again  select  the  atomic  weight,  which  like- 
wise is  an  experimentally  determined  quantity. 

In  plate  9  we  have  the  result  of  such  a  graphic  comparison  of 
atomic  volume  to  atomic  weight.  We  have  taken  as  abscissae 
(horizontals)  the  atomic  weights,  and  as  ordinates  (verticals) 
the  atomic  volume ;  the  point  of  intersection  of  these  two  lines 
(equal  to  the  numbers  a  and  V  according  to  the  scale  marked 


55 

on  the  diagram)  marks  the  place  or  point  of  the  element  con- 
sidered. 

To  find  the  place  or  point  of  the  diamond,  we  set  off  its  atomic 
weight  12,  according  to  scale  marked  on  the  base  of  the  diagram, 
to  the  right ;  erect  a  perpendicular  and  cut  off  hereof  the  length 
3.4  units  of  the  scale  of  volumes  marked  on  the  sides  of  the  dia- 
gram;  the  point  thus  determined  represents  the  diamond .  We 
have  marked  it  by  a  square  to  indicate  the  quadrivalence  of 
carbon. 

Since  carbon  also  occurs  lighter  as  graphite,  we  also  find  the 
atomic  volume  thereof  above  that  of  the  diamond.  In  the  same 
way  the  point  (full  back  circle)  marked  Ka  is  determined  by 
erecting  a  perpendicular  to  the  base  at  its  point  39  (the  atomic 
weight  of  Ka)  and  cutting  off  the  length  45.1  (the atomic  volume 
of  Ka.)* 

In  this  manner  every  point  marked  on  this  chart  has  been 
found  by  the  experimental  determination  of  the  atomic  weight 
and  atomic  volume  of  the  element  indicated  by  the  chemical  sym- 
bol near  the  point.  The  points  themselves  have  been  marked 
black  for  the  metals,  open  for  the  metalloids,  and  indicate  by 
their  size  and  shape  the  valence  of  the  element,  as  shown  near 
the  right  hand  lower  corner  of  the  chart. 

Finally,  the  points  marking  elements  of  any  one  genus  have 
been  joined  by  lines,  and  these  lines  are  designated  by  the  Greek 
symbol  of  this  genus. 

All  the  data  thus  graphically  (geometrically)  represented  in 
their  numerical  values  on  this  chart  are  facts  observed,  deter- 
mined in  the  course  of  many  years  by  the  physicists  and  chemists 
of  many  lands. 

These  facts  being  represented  geometrically,  we  can  study 
them  by  carefully  looking  at  them  with  our  eyes ;  this  is  the 
great  advantage  of  our  method  of  investigation.  Let  us  exam- 
ine this  chart  and  let  us  state  in  words  what  we  see. 


*  We  intended  to  insert  both  the  full  plate  (small  scale)  and  the 
lower  half  of  the  plate  enlarged,  but  have  concluded  to  print  the  latter 
only,  which  leaves  the  elements  Ka,  Rb,  Cs  (and  these  only)  beyond  the 
limits  of  our  plate. 


56 

The  most  striking  features  of  this  chart  are  the  following 
three :  — 

I.  The  line  of  atomic  volume  of  the  Kcdoids  rises   the   most 
abruptly  and  is  throughout  the  highest  of  all. 

II.  The  line  of  atomic  volume  of  the  Palladoids  and  Cuproids 
is  the  lowest  and  rises  the  slowest  of  all. 

III.  The  line  of  atomic  volume   of  the  Chloroids   is   almost 
midway  between  these  two  extremes. 

This  is  exactly  the  same  grouping  as  we  have  found  for  the 
fusing  point,  showing  a  like  relationship  of  constitution  as  proved 
by  the  fusing  point  lines. 

Beading  next  the  Greek  symbols  of  the  genera  upward  at  the 
left  margin  we  find  the  following  order  (adding  the  valence  in 
parenthesis) :  — 

Palladoids,  Cuproids,  Cadmoids  (2)  Styptoids  (3),  Adaman- 
toids  (4),  Phosphoids  (3),  Sulphoids  (2),  Chloroids  (1).  This 
is  exactly  the  order  in  which  the  genera  occurred  before  (for  fus- 
ing point)  and  in  which  we  have  placed  them  on  our  general 
charts.  Compare  Plates  6,7,9  and  others. 

The  place  of  the  cuproids  here  represents  heavy  monovalent 
elements  ;  but  only  silver  is  really  monovalent,  and  it  may  be  con- 
sidered that  for  these  very  dense,  most  strongly  metallic  elements, 
the  peculiarity  of  the  central  iron  group  in  the  next  lines  below  is 
already  marked  by  the  absence  of  a  definite,  constant  valence  of 
the  cuproids. 

As  to  the  direction  of  the  last  part  of  these  lines,  connecting  the 
last  two  elements  of  these  genera,  the  following  facts  are  appar- 
ent (omitting  of  course  these  lines  for  the  sulphoids  and  chlo- 
roids  because  the  fifth  members  thereof  have  not  yet  been 
discovered) : — 

These  lines  of  atomic  volume  are  nearly  parallel  and  but  very 
slightly  rising,  showing  almost  equality  of  atomic  volume  for  the 
last  two  members  of  each  genus  here  represented.  The  lines  for 
the  Sideroids  (Ru— Ir),  Palladoids  (Pd— Pt)  and  Cuproide 
(Ag — Au)  are  not  only  parallel,  but  also  horizontal,  forming  an 


57 

angle  of  zero  degrees  (with  the  base  of  the  plate).  For  all  these 
elements,  the  atomic  volume  of  the  last  two  members  of  each 
genus  specified  are  really  equal,  notwithstanding  their  enormous 
difference  in  atomic  weight. 

The  corresponding  lines  for  the  Cadmoids  (Cd — Hg)  and 
Styptoids  (In — Tl)  are  also  parallel,  but  rise  slightly,  forming  an 
angle  of  only  6  degrees  with  the  horizontal  base  of  the  plate, 
which  corresponds  to  a  rise  of  about  one  unit  on  the  atomic  vol- 
ume for  a  change  of  hundred  units  in  the  atomic  weight. 

The  corresponding  adamantoids  (Sn — Pb)  rise  a  little  faster, 
their  connecting  line  being  inclined  to  the  horizontal  base  under 
an  angle  of  about  7  degrees,  while  the  trivalent  relatively  negative 
phosphoids  (Sb — Bi)  form  a  straight  line  which  rises  under  about 
10  degrees. 

The  general  results  just  observed  concerning  the  near  equality 
of  the  atomic  volume  of  the  last  two  members  of  the  various 
genera  specified  confirms  anew  the  former,  observation  (for  fusing 
point)  that  in  the  higher  members  of  all  genera  the  physical 
properties  come  near  together,  only  the  chemical  character 
(valence)  remaining  distinct. 

This  confirms  the  former  conclusion,  that  the  higher  members 
must  result  from  the  lower  ones  by  the  addition  of  matter  of  the 
same  kind  (pantogen). 

Let  us  now  inspect  the  initial  part  of  the  lines  representing 
the  atomic  volume  of  the  different  genera. 

Here  we  may  first  take  note  of  the  very  striking  fact  that  the 
nullovalent  elements  (Argonoids)  are  found  almost  exactly  mid- 
ways between  the  monovalent  electropositive  kaloids  and  the 
monovalent  electronegative  chloroids.  There  can  be  no  doubt 
about  the  position  of  this  nullovalent  group  of  elements ;  it 
stands  where  our  formula  published  in  1874  placed  it,  and  where 
a  group  is  required  between  the  monovalent  electronegative  and 
positive  elements.  See  our  diagram  Plate  11  and  notice  the 
numerical  details  and  algebraic  formula  in  the  upper  right  hand 
corner  of  Plate  10. 

Looking  a  little  closer  into  this  left  quarter  of  our  plate  we 
find  the  three  elemental  gases  H,  O  and  N  quite  close  together, 
and  possessing  a  rather  large  atomic  volume  (about  15),  almost 


58 

equal  to  that  of  water  (18),  while  the  solid,  most  difficultly 
fusible  and  least  volatile  elements  C  and  Bo  also  are  near  each 
other,  but  very  much  below  the  three  gaseous  elements.  The 
monovalent  gas  Fl,  when  liquefied,  has  a  larger  atomic  volume 
than  the  other  three  liquefied  gases. 

Here  we  have  a  repetition  of  the  most  striking  discontinuity 
already  found  before  for  the  fusing  (and  boiling)  points  of  these 
elements  of  the  first  order.  We  also  here  merely  take  notice  of 
this  fact  now  strongly  re-enforced;  for  a  solution,  we  must  look 
to  a  later  chapter. 

We  must  here  notice  that  the  two  metallic  elements,  lithium 
and  beryllium,  are  placed  between  the  gaseous  and  solid  metal- 
loids. 

Having  found  the  location  of  the  initial  element  of  each  genus, 
we  may  next  trace  the  line  of  atomic  volume  of  the  initial  triads: 
Li— Na— Ka;  Be— Mg— Ca;  Bo— Al— Sc  ;  C— Si— Ti  for  the 
electropositive  elements  from  monovalent  to  quadrivalent  in 
chemical  character. 

We  see  at  a  glance  that  these  triad  lines  of  atomic  volume  are 
straight  lines  and  the  middle  element  marks  nearly  the  middle  of 
these  lines,  which  of  course  signifies  that  the  increase  of  atomic 
volume  from  the  first  to  the  second  is  about  the  same  as  the  in- 
crease from  the  second  to  the  third  element. 

Since  the  atomic  weight  increases  in  these  cases  by  the  same  (or 
very  nearly  the  same)  amount  16,  we  may  also  express  the  fact  of 
the  equal  increase  in  the  corresponding  atomic  volume  by  saying 
that  for  all  these  genera  the  connective  addition  of  16  to  the  atomic 
weight  produces  an  equal  increase  in  the  atomic  volume  in  each 
separate  genus. 

The  amount  of  this  increase  is  by  far  the  greatest  for  the  mono- 
valent kaloids ;  diminishes  greatly  as  the  valence  rises  to  two ; 
then  more  slowly,  being  smallest  for  the  tetravalent  genus.  This 
roughly  corresponds  to  the  fractions : 

t       *       »       i 

We  cannot  here  develop  the  reason  of  the  duplication  of  the 
increase  in  the  first  two  members,  nor  of  the  reduction  in  absolute 
amount  with  increasing  valence  ;  for  the  purpose  of  induction,  the 


59 

fact  is  the  main  thing  we  can  bring  out  in  this  short  popular 
exposition. 

But  we  may  be  permitted  to  refer  to  our  work  on  atomic  volume 
in  our  Programme  (1867),  our  second  Contribution  (1868),  our 
Note  X  (Acad.  Science,  Paris,  1891,  July  6)  in  which  the  general 
principle  is  established  that,  under  proper  restrictions,  prismatic 
atoms  possess  atomic  volumes  proportional  to  their  length. 

This  proves,  that  thejirst  two  additions  of  16  each  to  the  first 
member  of  the  initial  triad  is  made  in  the  direction  of  the  axis  of 
the  first  atom. 

That  is  to  say,  the  weight  16  added  to  Boron  11  joins  it  in  the 
direction  of  the  longitudinal  axis  of  the  boron  atom  (at  right 
angles  from  the  plane  of  the  three  valences),  yielding  the  atom 
of  aluminium ;  to  this,  in  turn,  the  next  increase  of  16  is  made 
in  the  same  direction,  so  ^hat  the  scandium,  aluminium  and 
boron  atoms  would  appear  in  a  longitudinal  projection  in  the 
following  manner :  — 

Bo  Bo 

Al  Bo— 16 

Sc  Bo— 16— 16 

Further,  the  reduction  of  the  increase  in  volume  with  the 
increase  in  valence  proves  equally  positively  that  the  original  or 
first  atom  shows  that  valence  in  virtue  of  its  structure,  and  that 
the  increase  is  added  in  the  same  manner. 

That  is,  the  divalent  Be  is  a  double  body ;  adding  16  means 
the  lengthening  of  each  of  these  two  bodies  by  8  ;  the  next  addi- 
tion is  again  twice  8. 

For  the  tetravalent  C  the  body  is  quadruple ;  the  addition  16 
means  one  addition  "of  four  to  each  of  these  four  parts  of  the 
carbon  atom  ;  and  so  on  for  all  other  elements. 

If  this  be  true,  certain  deviations  must  show  themselves  espe- 
cially in  the  trivalent  genera.  But  this  is  not  the  place  to  enter 
into  further  details.  Facts  of  this  kind  have  come  to  light  in 
preceding  parts  of  this  little  work. 

Comparing  next  our  charts  Plate  8  and  Plate  9 ,  we  see  that  the 
kaloids,  cadmoids,  styptoids  and  adamantoids  begin  with  a  triad, 


60 

exactly  as  here  brought  to  light ;  further,  that  the  other  genera 
do  not  begin  with  a  triad,  but  with  only  two  elements. 

Examining  our  chart  of  atomic  volumes,  we  notice  the  same 
striking  contrast;  for  the  initial  lines  of  the  chloroids,  sulphoids 
and  phosphoids  show  only  two  jioints  forming  a  straight  line, 
namely  in  the  above  order :  Fl — Cl ;  O — S  ;  N — P.  If  we  from 
the  second  (Cl,  S,  P)  pass  to  the  third  element  (Br,  Se,  As)  we 
have  to  turn  greatly  aside  from  the  first  line  joining  the  first  two 
elements,  and  we  have  in  each  case  to  turn  to  the  right. 

There  surely  are  only  two  parts  forming  a  prism  in  these  nega- 
tive elements,  namely,  theirs*  atom  and  the  first  addition  of  16. 
There  is  not,  and  there  cannot  be,  a  triad  for  these  genera  begin- 
ning with  the  first  element  of  the  same. 

In  these  three  genera  we  find  the  old  triads  beginning  with  the 
second  member,  namely,  Cl — Br — lo ;  S — Se — Te  ;  P— As — Sb. 
The  first  two  form  approximately  (sulphoids)  or  accurately 
(chloroids)  straight  lines.  The  notable  break  or  elbow  in  the 
phosphoids  is  associated  with  marked  allotropy ;  our  chart  shows 
connecting  lines  for  the  yellow  phosphorus,  and  also  gives  the  loca- 
tion of  the  red  and  black  phosphorus.  We  therefore  need  not 
enter  upon  further  detail  here. 

Now,  returning  to  the  genera  beginning  with  a  triad  (kaloids, 
cadmoids,  styptoids  and  adamantoids)  we  see  from  both  the  sec- 
ond and  the  third  member  a  triad  turn  off  to  the  right  also  under 
a  very  sharp  break  in  the  line  marking  the  atomic  volume  of  the 
initial  triad.  Thus  from  silicon,  the  triad  Si — Ge — Sn  starts 
under  an  angle  about  125  degrees  with  the  direction  C — Si — Ti. 
The  triad  Ti — Zr— Ce  from  Ti  breaks  off  from  the  same  line 
C — Si — Ti  under  about  the  same  obtuse  angle. 

The  same  break  we  notice  in  every  case ;  the  angle  varies,  but 
the  break  is  always  strongly  marked.  So  it  is  also,  as  above 
stated,  for  the  electronegatives  which  show  no  initial  triad ;  at 
Cl  the  triad  Cl — Br — lo  forms  an  angle  of  130  degrees  with  the 
initial  Fl — Cl.  Even  the  argonoids  show  this  character;  the 
line  Ar — Kr  forms  an  angle  of  140  degrees  with  the  line  Ne — Ar. 

This  angle  is  always  obtuse  for  the  upper  triad,  but  may  be 
acute  for  the  lower  triad.  Thus  the  upper  (light)  Ca — Sr — Ba 
starts  at  Ca  under  an  angle  of  150  degrees,  while  the  lower 


61 

(heavy)  triad  Mg — Zn — Cd  starts  at  Mg  under  an  angle  of  about 
85  degrees. 

Here  we  meet  again  the  question  as  to  the  relation  of  the 
cuproids.  The  lower  triad,  starting  from  Na,  could  only  consist 
of  Na — Cu — Ag,  and  would  accordingly  form  the  very  acute 
angle  of  40  degrees  with  the  line  Li — Na.  This  would  not  only 
be  a  very  curious  triad,  but  also  be  very  slenderly  connected  by 
the  very  long  line  Na — Cu  and  under  a  most  acute  angle  stated. 

We  must  here  again  conclude,  as  we  did  above,  that  the 
relationship  is  very  "  distant  "  and  "  shadowy,"  and  it  is  very 
much  overbalanced  by  the  closer  relationship  of  the  cuproids  to 
the  ferroid  group. 

We  must  now  consider  the  meaning  of  the  most  striking 
branching  of  the  middle  triad  volume  line  from  the  initial  steep 
volume  line  of  the  first  two  or  three  elements  of  each  genus.  In 
this  work  it  may  be  convenient  to  understand  a  few  generally 
neglected  facts,  which  already  in  our  Programme  of  1867  we 
have  expressed  in  very  simple  terms. 

The  atomic  volume  of  an  element  is  the  entire  space  occupied 
or  maintained  by  that  atom  ;  we  call  it  also  the  atostere.  The 
real  ponderable  element  atom  actually  fills  only  a  very  small  frac- 
tion of  this  atostere  in  the  gaseous  state,  and  even  in  the  solid 
state  fills  only  part  of  the  atostere ;  we  must  bear  this  in  mind  in 
all  our  considerations. 

The  space  filled  by  the  ponderable  atom  we  have  called  the 
atobar  (weight)  ;  its  length  the  atometer  (length)  and  its  cross- 
section  the  atomare  (area).  Programme  1867,  p.  6. 

Now  Plate  9  shows,  in  the  rise  of  the  initial  part  of  the  atomic 
volume  line,  the  increase  of  this  volume  proportional  to  the  ato- 
meter, as  we  have  above  found  ;  the  triad  lines  branching  off  to 
the  right  in  almost  parallel  direction  more  and  more  approaching 
the  horizontal  as  the  genera  descends  to  the  ferroids,  prove  there- 
by that  the  atobar  is  not  lengthened  in  the  last  three  elements  of 
the  different  genera,  but  remains  the  same  that  it  is  in  the  element 
from  which  the  triad  starts. 

Thus  the  line  of  atomic  volume  rises  rather  steeply  from 
Fluorine  to  Chlorine ;  but  from  this  last  element  it  passes  to  the 
right  in  an  almost  straight  line  nearly  parallel  to  the  base,  show- 


62 

ing  that  the  atomic  volume  of  Bromine  and  Iodine  is  nearly  the 
same  as  that  of  Chlorine. 

But  the  amount  of  material  added  is  twice  in  succession  three 
times  as  much  as  added  to  fluorine  to  form  chlorine,  which 
single  addition  greatly  increased  the  atomic  volume  of  chlorine. 

This  condition  is  quite  general,  as  our  Plate  shows,  for  all 
genera  of  elements  represented  on  the  same.  We  therefore  must 
conclude  that  the  atometer  of  the  last  three  elements  of  each  yenitx 
is  nearly  the  same  as  that  of  the  initial  element  of  the  middle  triad. 

But  this  conclusion  requires  that  the  relatively  large  amount  of 
matter  added  to  the  element  at  which  the  branch  starts  has  been 
placed  parallel  to  the  axis  of  the  atobar  of  that  initial  element  of 
this  middle  triad ;  it  has  enlarged  the  atomare,  and  not  lengthened 
the  atometer. 

This  is  precisely  what  we  concluded  from  the  study  of  the 
fusing  points  of  the  elements,  namely,  that  the  multiples 


times  the  weight  of  (nearly)  16  is  added  laterally,  not  in  axially 
to  the  lower  members  of  each  genus  of  elements. 

From  our  mechanics  of  the  three  states  of  matter  we  know 
that  in  the  liquid  state  the  atoms  revolve  around  the  longer  axis 
(for  which  the  moment  of  inertia  is  smallest)  the  atometer  of 
these  element  atoms  is  the  direction  of  their  axis  of  rotation,  and 
the  atomare  the  plane  of  that  rotation.  See  Notes  in  Comptes 
Rendus,  1873,  1875,  and  later.  Also  Principles,  1874. 

By  the  time  that  continued  heating  has  caused  fusion,  when  the 
atoms  freely  revolve  around  their  prismatic  axis  specified,  the 
cross-section  of  the  atostere  is  so  much  longer  than  the  atomare 
that  an  increase  of  the  latter  as  here  pointed  out  for  each  triad, 
will  be  insignificant. 

Using  the  diagrams  before  given  (Plate  10,  the  middle  right 
hand  side)  we  notice  that  the  radius  of  the  atobar  for  the 
first  member  of  the  triad  being  taken  as  unit,  that  of  the  third 
member  will  be  3  and  that  of  the  last  member  of  the  genus  not 
quite  3.5.  The  radius  of  the  atobar  for  Pb  is  therefore  only 
one  sixth  greater  than  for  tin,  and  has  increased  in  the  same  pro- 
portion in  the  other  genera. 


63 

Such  an  increase  of  the  nucleus  or  atobar  can  have  but  a  small 
effect  upon  the  cross-section  of  the  atostere ;  but  the  length  of 
the  atobar  (or  the  atometer)  measures  the  length  of  the  revolving 
atobar  which  determines  the  height  of  the  cylindrical  space 
(atostere  or  atomic  volume)  of  the  element  in  the  liquid  state. 

This,  we  trust,  will  suffice  to  make  the  inductive  results  theo- 
retically understood ;  here  the  main  thing  is  the  fact  —  the 
theoretical  explanation  is  of  secondary  importance. 

RADIO    ACTIVE    ELEMENTS. 

Supposing  the  constitution  of  the  chemical  elements  be  exactly 
as  here  confirmed  by  the  study  of  their  atomic  volume  (or  specific 
gravity)  and  as  first  was  found  by  our  study  of  their  fusing 
points ;  can  we  indicate,  from  the  entire  system  of  chemical  ele- 
ments, any  genus  that  will  admit  more  freely  of  oscillation  of  its 
constituent  parts,  than  the  others? 

Calling  the  first  or  initial  element  in  each  genus  a  monad  (True 
Atomic  Weights,  1894,  p.  213),  and  the  next "  elements  grown 
from  these  by  the  addition  once  or  twice  of  16,  in  the  axis  of  the 
monad  the  heavy  dyads  (sulphoids)  and  the  light  dyads  (kaloids) 
we  have  distinguished  the  following  elements  formed  by  the  lat- 
eral addition  of  three  times  this  mass  (of  about  16)  triads  and  the 
last  element  resulting  from  the  further  addition  of  six  times  this 
mass  we  have  called  hexads.  See  Plate  8. 

We  have  also  called  special  attention  to  the  fact  that  generally 
these  triads  and  hexads  do  not  show  an  increase  in  atomic  weight 
of  the  full  limiting  amount  of  3  times  16  or  48  units  for  the  triads 
and  6  times  16  or  96  for  the  hexads  ;  but  several  units  less.  We 
have  also  referred  this  peculiarity  to  the  well  known  fact  of 
organic  chemistry,  that  loss  in  iveight  of  the  combining  radical 
produces  a  more  intimate  chemical  combination. 

Thus  Methane  does  not  combine  ;  it  is  not  a  radical,  but  a  gas  ; 
its  atomic  weight  is  16.  One  hydrogen  removed  gives  methyl 
which  is  a  radical  of  valence  one  ;  its  weight  is  15.  The  next 
radical,  weighing  14,  has  a  valence  two,  forming  the  so-called 
double  links  or  bonds.  Next  we  have  the  tri-valent  radical  13, 
followed  by  tetravalent  element  carbon  weighing  12. 


64 

We  herewith  may  compare  the  adamantoids.  Silicon  28,  the 
dyad,  increases  but  45  to  form  germanium,  which  again  increases 
45  to  form  tin,  which  latter  increases  not  even  twice  this  amount 
(90),  but  one  unit  less  (89)  to  form  lead.  Here  we  have  in  the 
triads  each  3  units  of  atomic  weight  less  than  would  result  from 
an  addition  of  the  full  48  units,  representing  3  times  the  funda- 
mental increase  of  16.  The  step  from  tin  to  lead  takes  place 
with  a  loss  of  7  units ;  for  only  89  units  are  added,  instead  of 
96.  Compare  True  At.  Wghts.,  p.  220. 

We  cannot  here  state  how  many  real  atomic  ties  these  specified 
numbers  represent ;  that  will  depend  upon  the  atomic  weight  of 
pantogen,  which  we  do  not  need  to  consider  here.  But  it  will 
be  admitted,  that  if  an  atom  of  hydrogen  consists  of  the  least 
possible  number  of  pantogen  atoms  (which  is  two),  the  above 
numbers  of  units  of  atomic  weights  would  represent  double  that 
number  of  atomic  ties. 

As  a  rule  we  therefore  may  say,  that  the  greater  the  difference 
from  48  and  96  in  the  increase  of  atomic  weight  of  the  triads  and 
hexads,  the  more  firmly  the  atoms  of  the  corresponding  elements 
are  tied,  and  the  less  chance  there  can  be  for  intra-atomic  vibra- 
tions of  any  kind. 

The  central  portions  of  our  system  containing  the  trivalent 
and  tetravalent  elements,  show  an  increase  of  44  to  45,  and  88 
to  90  only  in  the  styptoids,  adamantoids  and  phosphoids  (see 
preceding  tables).  Equally  low  are  the  additions  in  the  Pal- 
ladoids  and  Cuproids. 

For  the  divalent  cadmoids  we  find  an  average  of  44  for  the 
triads  and  88  for  the  hexad ;  for  the  divalent  sulphoids 
we  have  45  and  47  (average  46)  for  the  triads,  no  hexad  yet 
being  known. 

For  the  monovalent  kaloids  we  have  47  and  for  the  chloroids 
about  46  ;  for  neither  of  these  we  know  the  hexad. 

Evidently,  all  these  genera  of  elements  are  held  in  their  higher 
atoms  (triads  and  hexads)  by  ties  equivalent  at  the  lowest  to  one 
unit  of  atomic  weight  in  the  triads  (kaloids  and  chloroids). 
Quite  a  different  condition  of  fact  obtains  for  the  calcoids. 

Taking  calcium  as  40,  we  find  a  full  increase  of  48  to  strontium 
and  even  49  next  to  Barium.  Unfortunately  the  experimental 


65 

determinations  of  the  atomic  weight  of  strontium  and  barium 
are  not  above  question.  Nevertheless  the  accepted  values  give 
no  room  for  any  ties  binding  the  constituent  triad-additions  in 
any  way  atomically ;  they  seem  to  be  merely  in  molecular  com- 
bination. 

Accordingly,  we  may  expect  a  wider  susceptibility  to  intra- 
atomic  vibrations  in  the  atobars  of  the  calcoids  than  in  the  atobars 
of  any  of  the  other  elements.  Common  experience  has  long  made 
chemists  familiar  with  the  remarkably  brilliant  light  of  the  ignited 
oxides  of  this  group. 

In  the  titanoids  we  find  somewhat  similar  conditions.  Tita- 
nium exceeds  the  estimated  atomic  weight  44  by  4  units  (indicat- 
ing mobility  at  the  second  link  of  this  dyad),  and  cerium  and 
thorium  are  the  essential  radiators  in  the  Welsbach  light. 
Unfortunately,  the  atomic  weight  determinations  in  this  group 
are  also  far  from  satisfactory. 

But  it  will  be  immediately  recognized  that  thorium  is  an  ele- 
ment of  pronounced  radio  activity. 

The  Molybdoids  increase  by  44  and  89  from  chromium  to 
molybdenum  and  wolframium.  If  uranium  were  to  be  placed 
in  this  group  it  would  show  an  enormously  high  increase  of  55 
for  a  third  triad  ;  but  such  an  element  we  cannot  accept,  there- 
fore uranium  cannot  belong  to  the  molybdoids. 

Accordingly,  uranium  will  have  to  be  placed  as  one  of  the 
heaviest  of  the  class  of  the  metals  of  the  rare  earths,  and  thus 
fall  diagonally  in  line  with  the  radio-active  thorium  which  is 
supposed  to  have  an  atomic  weight  9  less  than  that  ascribed  to 
uranium.  See  Plate  6. 

This  agrees  admirably  with  the  fact  that  uranium  and  thorium 
both  are  pronounced  radio-active  elements. 

The  hexad  of  the  calcoids  is  the  supposed  element  radium, 
which  possesses  radio  activity  in  the  highest  degree.  We  have 
already  considered  its  supposed  atomic  weight.  The  value  given 
by  the  Curies  (225)  was  shown  to  be  low,  while  that  indicated 
by  its  spectrum  (258)  is  quite  high. 

Any  value  above  232  (for  Ba  136)  or  234  (for  Ba  138)  would 
imply  the  full  number  of  96  units  added  to  the  barium  to  obtain 
the  corresponding  hexad. 

5 


66 

If  the  atomic  weight  of  radium  shall  be  found  at  least  233, 
there  cannot  be  any  chemical  ties  in  this  hexad ;  its  addition  of 
six  times  16  units  is  not  restrained  by  chemical  atomic  ties  from 
oscillatory  motions. 

But  we  do  not  wish  to  go  too  far  on  this  ground.  We  need 
very  excellent  atomic  weight  determinations  to  form  a  basis  for 
this  structure.  The  facts  as  known  bring  the  radio  activity  of 
these  three  elements  in  so  close  relation  that  the  atomic  weight 
determinations  ought  to  be  undertaken  in  a  truly  rational 
manner. 

THE    DECOMPOSITION    OF    THE    ELEMENTS. 

Starting  with  a  substance,  supposed  to  be  a  compound  of 
*'  radium,"  an  English  chemist  has  recently  obtained  an  "  ema- 
nation" which  he  supposes  derived  from  the  supposed  element 
radium.  Another  very  noted  English  chemist  has  observed  the 
44  helium  lines  "  in  this  emanation,  at  least  for  a  short  time, 
after  which  there  remained  —  it  is  not  stated  what. 

Again,  a  noted  physicist  of  one  of  the  famous  old  English 
universities,  has  determined  the  *'  mass  "  of  certain  **  radiations," 
supposed  to  be  "  electrons  "  and  finds  this  "  mass  "  of  the 
electrical  radiation  about  one  thousandth  of  the  mass  of  an  atom 
of  hydrogen.  Hence  —  electricity  is  moving  mass,  and  matter  is 
composed  of  electricity,  about  a  thousand  "electrons"  to  one 
atom  of  hydrogen. 

These  contrasting  views  remind  us  of  the  conditions  two  cen- 
turies ago,  quaintly  expressed  by  Voltaire,  who  left  the  world 
full  of  matter  in  France,  but  found  it  to  be  absolutely  empty 
upon  his  arrival  in  England.  The  "  energetic  "  chemist  of 
Leipzig  denies  matter ;  the  physicist  of  Cambridge  weighs  elec- 
trical energy  in  ponderable  atoms  of  hydrogen. 

In  the  scientific  literature  of  the  day,  these  most  astonishing 
conclusions  are  accepted  without  much  questioning.  Here  in 
St.  Louis,  in  the  great  "  Government  Building,"  thousands  of 
people  are  told  by  a  young  "  lecturer  "  twice  a  day,  "  at  the 
expense  of  the  Government "  these  same  conclusions  as  prac- 
tically established  facts ;  adding  a  nice  determination  of  the 
' '  life  of  an  atom  ' '  by  giving  it  a  "  round  number  of  thousand 


67 

years  "  so  that  the  audience,  mostly  ladies,  will  not  witness  the 
agony  of  any  expiring  atom. 

To  present  to  the  general  public  as  established  scientific  facts 
a  lot  of  fairy  tales,  illustrated  by  experiments  of  a  taking  kind, 
properly  "  all  in  the  dark,"  is  a  sort  of  missionary  work  in 
"  modern  science"  that  to  some  of  us  will  appear  a  very  ques- 
tionable enterprise,  especially  when  carried  out  at  national 
expense. 

"  Our  Government"  in  this  great  building  is  instructing  its 
people  in  a  very  queer  way  even  as  to  simple  plain  facts  of  com- 
mon observation  —  of  course,  always  in  splendid  form,  since 
Uncle  Sam  has  money  to  burn  by  the  million.  Surrounded  by 
the  collection  of  chemically  most  important  cosmical  materials 
stands  in  elegant  frame  a  big  and  beautifully  finished  map  of  the 
United  States,  showing  by  blue  stars  where  these  meteorites  have 
been  found,  and  by  red  stars  where  they  have  been  seen  to  fall. 

The  town  of  West  Liberty,  Iowa,  is  marked  by  such  a  red  star  ; 
but  it  is  a  notorious  fact,  that  no  meteorite  was  ever  seen  to  fall  at 
or  near  that  town,  nor  was  any  meteorite  ever  found  at  or  near 
West  Liberty,  Iowa. 

In  its  official  "  Catalogue  of  the  Meteorite  Collection  of  the 
United  States  National  Museum  to  January  1,  1902  "  (page  685), 
published  by  the  Smithsonian  Institution,  "  for  the  Increase  and 
Diffusion  of  KNOWLEDGE  among  Men  per  Orbem  "  we  read  West 
Liberty,  Iowa  County,  Iowa,  as  the  locality.  But  outside  of  the 
National  Museum  and  the  Smithsonian  Institution  nobody  knows 
of  any  town  or  post  office  "  West  Liberty  "  in  Iowa  County, 
Iowa. 

Examining  this  grand  official  Meteorite  Map  of  the  United 
States  a  little  further,  we  find  Iowa  County,  Iowa,  without  any 
meteorite  mark;  yet  it  is  known  in  scientific  circles  throughout 
the  world,  that  one  of  the  grandest  meteors  was  seen  on  the  even- 
ing of  February  12,  1875,  throughout  the  Northwest,  and  that 
many  large  meteorites  fell  on  that  occasion  in  IOWA  COUNTY,  IOWA, 
mainly  in  the  Amana  Colony.  I  have  personally  collected  and 
studied  about  one  hundred  of  these  meteorites,  the  aggregate 
weight  of  which  is  much  over  two  hundred  kilograms,  or  about 
five  hundred  pounds. 


68 

Such  is  "  Government  Science,"  represented  at  our  World's 
Fair.  Is  State-Science  to  be  as  bad  as  history  claims  to  have 
proved  the  State  Church  ? 

But  it  is  useless  to  contend  against  the  scientific  errors  prom- 
ulgated by  the  millions  appropriated  by  our  National  Govern- 
ment whether  in  regard  to  Radium,  meteorites  or  atomic  weights. 
Though  profoundly  convinced  that  the  elements  are  complex 
and  not  simple  in  their  nature,  but  built  up  from  one  single  kind 
of  matter,  and  though  I  have  now  worked  carefully  for  half  a 
century  to  get  "  more  light "  on  the  precise  complex  structure  of 
these  elements  by  means  of  a  thorough  study  of  their  physical, 
chemical  and  crystallographic  properties  by  the  aid  of  the  known 
laws  of  general  mechanics,  I  must  confess  that  I  have  been 
unable  to  accept  any  of  the  so-called  experimental  demonstrations 
of  the  chemical  decompositions  of  any  one  of  our  elements. 

Let  us  examine  the  conditions  of  a  possible  decomposition  of 
the  chemical  elements  from  our  point  of  view. 

First,  we  may  admit  that  there  is  some  valuable  evidence 
that  certain  genera  of  the  elements  are  less  rigidly  constructed 
than  the  great  majority  thereof ;  such  a  group  of  elements  we 
have  pointed  out  in  the  higher  metals  of  the  rare  earths. 

The  keen  chemical  sense  of  Schiitzenberger  directed  his  work 
to  this  very  group. 

Second,  the  "  complex  16  "  which  we  have  found  so  promi- 
nent in  the  structure  of  the  chemical  elements,  and  which  is 
laterally  combined  by  ties  of  different  firmness  (reminding  us  of 
the  different  bonds  in  our  modern  organic  compounds),  may 
possibly,  in  some  cases,  be  "  broken  up"  and  then  most  likely 
yield  some  sub-multiple  thereof,  possibly  the  nullovalent  element 
of  atomic  weight  four,  which  we  call  helium. 

But  what  energy  will  it  require  to  loosen  one  of  these  bars  and 
to  break  it  up  ?  It  sometimes  seems  as  if  our  most  emphatic 
chemical  advocates  of  "energetics,"  who  even  go  so  far  as  to 
deny  the  existence  of  matter,  are  forgetting  some  of  the  funda- 
mental facts  of  the  conservation  of  energy. 

In  my  Elements  of  Chemistry  (1871)  and  in  my  Principles 
(1874)  I  have  tried  to  represent  chemical  energy  by  a  difference 
in  level ;  the  diagram  shows  hills  of  the  metals  down  the  steps  of 


69 

which  chlorine  flows  as  water  flows  down  over  mountains  and 
cataracts.  I  called  it  the  chlorine  cataract  and  gave  the  relative 
heights  according  to  well  known  determinations.  Monsieur 
Berthelot,  in  a  letter  of  March  16,  1875,  on  the  "Principles  " 
commended  the  presentation  of  this  general  topic  very  especially. 
I  trust  he  will  pardon  my  mention  of  this  fact. 

I  am  here  reminded  of  M.  Bertlielot  because  I  pointed  out  the 
the  mechanical  significance  of  a  fact  which  he  first  had  specially 
called  attention  to,  namely  the  radical  difference  presented  by 
the  specific  heat  of  elements  and  compounds.  See  my  Note 
XXIII  presented  by  M.  Berthelot  on  the  25th  July,  1892,  to  the 
Academy  of  Sciences  of  Paris.* 

In  the  following  words  I  explained  this  radical  difference 
between  elements  and  compounds  mechanically :  — 

"  In  chemical  compounds,  the  chemical  atoms  are  contained  as 
"  integral  individuals,  retaining  their  own  proper  motion  of  vibra- 
' '  tion ;  but  the  atoms  of  the  true  chemical  elements  are  solid  or 
"rigidrf  bodies  of  which  the  constituent  atoms  have  no 
"  individual  motions." 

In  other  words,  the  constituent  atoms  of  pantogen  have  lost 
their  mechanical  individuality  by  being  rigidly  united  to  a  single 
body  (the  element  atom)  ;  the  individual  pantogen-atoms  do  not 
separately  vibrate,  have  no  individual  motion  of  vibration  or  of 
any  other  kind ;  the  element-atom  is  one  rigid  mass.  This  is 
demonstrated  by  the  specific  heat  determinations  of  the  elements 
here  involved. 

In  a  letter  to  the  perpetual  Secretary  I  indicated  (at  the  time) 
the  enormous  expenditure  of  energy  that  would  be  required  to 
effect  the  separation  of  these  pan-atoms  or  the  association  of  the 
element  atoms.  Possibly  we  shall  be  able  to  accomplish  this  by 
means  of  electrical  energy,  some  time ;  but  there  seems  to  be  no 
immediate  prospect  of  doing  so.  At  least  I  cannot  find  any 
experiment  having  accomplished  this. 


*  Comptes  Rendus,  Tome  115,  p.  239;   1892.  — This  Note  was  repub- 
lished  in  Chemical  News,  London  Vol.  68,  p.  171 ;   1892. 

t  The  misprint "  liquides  "  for  "  rigides  "  in  the  C.  R.  is  very  annoying. 


70 

I  am  astonished  at  the  present  utter  disregard  of  the  funda- 
mental laws  of  physics  and  mechanics  which  successive  genera- 
tions of  great  men  have  established  from  Galileo,  through 
Huyghens,  Newton,  Leibnitz,  to  the  much  praised  modern 
Clausius,  Mayer  and  Helmholtz.  I  had  the  honor  of  a  personal 
acquaintance  with  Colding,  of  Copenhagen,  whose  famous  tribo- 
meter  first  proved  the  relation  between  heat  and  mechanical  work 
here  involved. 

Now  I  must  insist  that  to  effect  a  chemical  decomposition  of  a 
combination  more  intimate  than  that  of  the  elements  with  one  an- 
other will  require  an  enormously  greater  expenditure  of  energy 
than  the  decomposition  of  water. 

The  decomposition  of  water,  or  sodium  chlorides,  requires  an 
enormous  amount  of  energy  as  compared  to  that  required  to 
decompose  complex  organic  substances.  Yet,  while  some  of  these 
latter  compounds  decompose  by  contact  with  water,  we  are 
expected  with  our  most  noted  chemical  philosophers  of  the  day 
to  accept  that  sodium  chloride  also  decomposes  by  such  mere 
contact  (solution).  Professor  Winkler  has  recently  called  atten- 
tion to  the  fact  that  Crookes  pretends  by  mere  treatment  with 
ether  to  separate  certain  uranium  compounds,  the  radio-active 
from  the  non-active. 

But  enough.  There  has  not  yet  been  presented  any  experi- 
mental evidence  of  any  decomposition  of  any  chemical  element, 
so  far  as  I  am  able  to  judge. 

I  shall  be  delighted  to  recognize  such  decomposition  as  soon  as 
it  shall  have  been  accomplished ;  for  it  will  confirm  the  funda- 
mental principle  of  my  mechanics  of  the  atom,  and  greatly 
encourage  further  work  in  this  science. 

In  conclusion  it  may  not  be  amiss  to  recollect  the  striking  dis- 
appointment of  the  chemists  who  almost  half  a  century  ago  experi- 
mentally tried  to  obtain  Ethyl  and  Methyl.  The  reaction  took 
place  exactty  as  anticipated  —  but  of  course  these  radicals  did 
not  appear  in  the  manner  expected:  they  appeared  necessarily 
mutually  combined  as  saturated  hydrocarbons. 

Accordingly,  when  we  shall  have  decomposed  the  higher  ele- 
ments and  go  to  gather  up  the  pantogen  —  we  may  find  some 
simpler,  less  complex  elements,  especially  helium  and  hydrogen. 


71 


THE       IMPORTANCE      OF      ANOMALIES       IN     THE      DETERMINATION      OF 
THE    FORM    OF    THE    ATOMS. 

It  lies  beyond  the  plan  of  this  popular  introduction  to  give 
special  information  on  the  determination  of  the  form  of  the  atoms 
of  compounds  by  means  of  the  thermometer ;  most  of  my  NOTES 
published  in  the  Comptes  Rendus  contain  applications  of  the 
principles  already  set  forth  in  the  first  one  of  1873.  In  the  BEI- 
TRAEGE  of  1872  the  general  principles  were  already  expressed  by 
general  formula.  In  my  Principles  1874  this  subject  was  also 
quite  broadly  presented  ;  so  also  in  my  General  Chemistry  of  1897. 

Referring  to  this  extended  series  of  publications  for  details,  I 
shall  here  only  attempt  to  show  two  of  the  most  interesting 
and  most  important  anomalies  according  to  the  Rule-of -Three 
theory  of  Kopp  which  still  flourishes  in  Germany. 

When  Hermann  Kopp  in  1872  kept  my  papers,  refer  red  to  him 
by  the  German  Chemical  Society,*  he  thus  perpetuated  his  Rule- 
of -Three  Theory  —  and  kept  German  Chemistry  stationary,  and 
left  German  Chemists  in  ignorance  on  this  most  important  field 
of  investigation.  Even  Traube  in  his  recent  work  (Physikal. 
Chemie,  1904)  remains  sixty  years  behind,  and  does  not  seem 
to  have  any  knowledge  whatever  of  the  work  of  half  a  century. 

The  most  striking  anomaly  in  the  view  of  this  stagnant  Ger- 
man school  of  Kopp  is  the  lowering  of  the  fusing  or  boiling  point 
by  an  increase  of  atomic  loeight.  We  have  seen  this  "  anomaly  " 
to  mark  the  metallic  genera  of  the  elements. 

In  order  to  give  a  couple  of  examples  of  our  work  done  on  this 
ground,  we  print  here  Plates  12  and  13  from  the  first  part  of  our 
special  work  on  the  mechanics  of  the  three  states  of  aggregation, 
which  was  really  intended  to  fonn  part  of  this  book,  but  had  to 
be  omitted  for  lack  of  time. 

In  Plate  12  we  show  a  series  of  the  lowering  of  the  fusing  point 
by  an  increase  of  the  atomic  weight,  while  in  Plate  13  we  give  a 
most  striking  case  of  the  same  kind  for  the  boiling  point. 

The  Plates  give  really  all  the  necessary  information,  and  con- 
stitute striking  cases  of  our  method  of  geometrical  investigations 


See  letters  and  documents  in  my  Beitraege,  edition  1892. 


72 

in   physical  chemistry.     Only  a  few  general  explanations   may 
here  be  added. 

FUSING    POINT    ANOMALY. 

In  Plate  12  the  upper  oblique  heavy  line  (almost  straight) 
connects  the  fusing  points  of  the  most  important  Acetamids;  the 
formula  is  given  below  the  word.  The  one  dash  indicates  that 
the  acetamid-radical  is  monovalent. 

Below,  and  almost  parallel  hereto,  is  found  the  line  connecting 
the  fusing  points  of  the  Formamids,  in  the  same  manner. 

The  more  steep  dotted  lines  represent  the  positive  radicals 
(hydrogen,  phenyl,  phenmethyl,  phenethyl),  the  chemical  formula 
of  which  are  also  given  on  the  plate.  It  will  be  noticed,  that 
these  four  lines  are  also  very  nearly  parallel. 

By  two  such  systems  of  lines,  we  can  determine  the  fusing 
point  of  compounds  not  yet  known.  Even  the  fusing  point  of 
phenacetin  was  fairly  well  determined  from  acetamid  and  acetani- 
lid  before  it  had  been  made. 

Every  point  here  represented  shows  the  absurdity  of  the  school 
of  Kopp  still  dominant  in  Germany. 

However,  the  changes  thus  far  spoken  of  may  be  called  normal 
as  to  sign,  for  the  fusing  point  rises  with  increasing  atomic 
weight. 

But  it  does  not  increase  at  a  fixed  ratio,  for  the  full  drawn 
lines  of  the  negative  radicals  are  much  less  steep  than  the  dotted 
lines  of  the  positive  radicals. 

If  we  were  to  imitate  the  most  popular  German  leader  in  phys- 
ical chemistry,  we  might  say  the  Choneutism  of  the  negative 
radicals  is  much  in  excess  of  the  Choneutism  of  the  positive 
radicals.  It  might,  perhaps,  be  more  philosophical  to  use  the 
term  Choneutotropic  ;  I  shudder  at  the  responsibility  of  deciding 
so  profound  and  weighty  a  question. 

But  let  us  get  out  of  the  philosophic  atmosphere  of  Leipzig  and 
consider  the  facts  before  us.  By  a  simple  measurement  we  find 
that  at  the  point  phenacetin  the  line  marked  negative  radical 
forms  an  angle  of  14  degrees,  while  the  line  marked  positive 
radicals*  is  inclined  70  degrees  to  the  base  or  atomic  weight 


*  Along  the  line  marked  negative,  the  positive  radicals  vary. 


73 

abscissa.     We  also  notice  that  the  temperature  scale  numerically 
is  exactly  half  the  atomic  weight  scale. 

Since  now  the  tangent  of  14  degrees  is  0.25  and  that  of  70 
degrees  is  2.75,  the  increase  in  fusing  point  per  hundred  in 
atomic  weight 

is       50  degrees  C.  for  the  positive  radicals, 
but  550       "         "       "       negative      " 

To  return  for  just  a  moment  to  Leipzig  we  might  say  that 
choneutropic  force  of  the  negative  radicals  is  eleven  times  as 
great  as  that  of  the  positive  radicals  —  and  then  rest  again. 

But  leaving  nonsense  (I  mean  to  say,  modern  scientific  phil- 
osophy of  physical  chemistry)  aside,  we  simply  must  state  that 
the  much  greater  steepness  of  the  dotted  fusing  point  lines  shows 
that  the  fusing  point  rises  with  an  equal  increase  of  atomic  weight 
eleven  times  as  much  for  a  change  in  negative,  as  for  an  equal 
change  in  positive  radical.  There  certainly  is  no  change  for  the 
"  rule  of  three  "  here. 

But  perhaps  it  is  the  atomic  weight  of  these  radicals  that  in- 
fluences these  remarkable  relations.  The  atomic  weight  of  the 
positive  radical  phenethyl  (of  which  the  full  formula  is  given  on 
the  plate)  is  121  while  the  atomic  weight  of  the  negative  radical 
acetarnide  (also  given  on  the  plate)  is  58.  This  is  roughly  one- 
half  of  the  first.  Most  assuredly  nothing  comparable  to  the  ratio 
one  to  eleven. 

But  if  so  great  numerical  differences  occur  as  to  rate  we  ought 
not  be  surprised  to  find  even  the  sign  of  the  change  becomes 
reversed.  So  it  does  in  fact. 

Looking  at  the  dot  marked  Phenacetin,  we  notice  a  faint  line 
drawn  from  it  obliquely  down  to  the  right,  on  which  a  dot 
(fusing  point)  marked  Me  is  entered.  Further  down  this  line  we 
find  an  arrow  pointing  down  and  marked  Et. 

This  means  that  if  in  the  acetamide  radical  of  phenacetin  the 
last  atom  of  hydrogen  is  replaced  by  methyl,  the  fusing  point  is 
lowered  to  the  point  just  specified  and  marked  Me,  while  if  the 
same  were  replaced  by  Ethyl  it  would  lower  about  as  much  again 
and  fall  below  the  margin  of  our  plate. 

By  in  this  manner  increasing  the  atomic  weight  of  phenacetin 


74 

by  14,  the  fusing  point  falls  almost  one  hundred  degrees  ;  if  the 
increase  of  the  atomic  weight  is  doubled,  the  decrease  is  also 
roughly  doubled. 

If  we  turn  to  the  older  compound  Acetamid  we  find  on  our 
plate  two  lines  drawn  therefrom  to  the  right  and  downward, 
showing  a  rapid  fall  of  fusing  point  with  increasing  atomic 
weight,  namely  — 

1,  the  fall  drawn  line  marked  by  the  black  circles:   Me,  Et, 
Pr  represents  the  falling  fusing  points  of  Acetamid  in  which  the 
last  (amid-)  hydrogen   is   successively  replaced   by  the  radicals 
Methyl,  Ethyl  and  Propyl  which  increase  the  atomic  weight  by 
14,  28,  42  respectively;  and 

2,  the  dotted  line  marked  by  open  circles  Fo,  Ac  represents 
the   corresponding  substitutions   by  the   acid  radicals   Formyl, 
Acetyl,  increasing  the  atomic  weight  respectively  28,  42. 

It  will  also  be  noticed  that  the  difference  between  Ethyl  and 
Formyl  substitution  and  between  that  of  Propyl  and  Acetyl  is 
but  very  moderate;  the  corresponding  increase  in  atomic 
weight  being  for  the  first  28  and  for  the  second  42.  Nevertheless 
there  is  a  difference  in  the  results,  so  that  even  this  is  not  a 
simple  matter  of  atomic  weight.  The  rule  of  three  finds  no  rest- 
ing place  anywhere  hereabouts. 

From  what  has  been  shown  it  appears  that,  as  a  matter  of  fact, 
the  fusing  point  may  rise  slowly  or  rapidly,  and  it  may  even  fall 
rapidly  for  a  given  increase  of  the  atomic  weight. 

This  may  be  called  a  "  constitutional  "  difference,  and  not  an 
"  additive"  difference  and  the  Leipzig  school  would  rest  while 
we  would  know  nothing  about  it.  Even  the  fact  <i*  xm-li  has 
never  been  brought  out  as  strikingly  as  here  in  our  graphical  repre- 
sentation which  we  suppose  to  be  new ;  we  have  used  it  for  years. 

It  is  just  this  sort  of  anomalies  that  are  helpful  to  the  true 
investigator,  for  they  lead  to  the  truth  after  having  shown  them- 
selves inexplicable  on  all  common  suppositions. 

By  just  such  cases  the  rotation  of  the  atom  in  the  liquid  state 
is  demonstrated  to  be  around  the  natural  axis  for  which  the 
moment  of  inertia  is  a  minimum.  The  series  of  publications 


75 

introduced  must  be  consulted  by  those  who  would  study 
this  subject  more  thoroughly.  Here  in  this  popular  out- 
line, we  merely  wished  to  impress  upon  the  reader  that  really 
something  worth  consideration  has  been  done  in  this  field,  though 
in  the  words  of  Ostwald  (Electrochemie,  1896,  p.  879)  "the 
"  influence  of  a  few  men  controlling  scientific  opinion  *  *  * 
' '  made  the  consideration  of  the  work  *  *  *  to  be  regarded 
"  as  useless." 

BOILING     POINT    ANOMALY. 

On  Plate  13  we  give  a  striking  case  of  the  same  general  char- 
acter for  the  boiling  point.  All  necessary  data  and  formulae  are 
entered  upon  the  plate,  which  should  be  studied  with  special  care, 
since  we  can  only  devote  very  little  space  to  it  here  in  the  text. 

On  the  lowest  line  1  marks  the  observed  boiling  point  of  water  ; 
2  that  of  sulphuretted  hydrogen  also  observed  ;  3  the  correspond- 
ing compound  of  selenium,  also  observed;  4  that  of  tellurium 
by  our  graphical  interpolation. 

It  is  a  commonly  known  (but  very  rarely  stated)  anomaly,  that 
the  boiling  point  of  water  is  almost  180  degrees  higher  than  the 
boiling  point  of  hydrogen  sulphide ;  for  the  atomic  weight  of 
oxygen  is  16  and  that  of  sulphur  is  double  the  same,  32,  which 
would  according  to  Kopp  and  his  German  school  of  to-day 
require  the  opposite  character  and  much  less  in  amount. 
When,  however,  this  S  next  is  replaced  by  the  heavier  atoms  Se 
and  Te,  the  boiling  point  changes  normally  by  a  very  gradual 
rise. 

It  will  be  seen  further  on  our  plate,  that  when  one  atom  of 
hydrogen  of  the  water  is  replaced  by  an  alcohol  radical,  the 
anomaly  remains,  but  greatly  diminishes  in  amount  for  the  thus 
resulting  ALCOHOLS. 

Need  I  say  that  we  have  here  facts  comparable  to  the  gradual 
diminution  of  the  contrast  or  discontinuity  so  strongly  marked  in 
the  succeeding  orders  of  the  elements  ? 

If  now  also  the  second  atom  of  hydrogen  of  the  water  be 
replaced  by  another  alcohol  radical,  so  as  to  obtain  the  ETHER, 
the  anomaly  has  not  only  disappeared,  but  the  increase  from  1  to 
2,  that  is,  from  oxygen  to  sulphur  is  much  more  considerable  than 


76 

the   increase  from   sulphur   to  selenium,  and  from  selenium  to 
tellurium. 

Indeed,  the  boiling  point  lines  for  corresponding  alcohols  and 
ethers  are  concordant  for  S,  Se,Te,  but  symmetric  for  oxygen: 
rapidly  descending  for  alcohol,  rapidly  ascending  for  the  ethers, 
with  the  increasing  atomic  weight  from  oxygen,  16  to  sulphur,  32. 

These  conditions  are  an  exact  repetition  of  what  we  have  found 
when  studying  the  fusing  and  boiling  points  of  the  elements. 

No  more  striking  facts  can  be  found  in  any  part  of  physical 
chemistry ;  but  still,  these  marvelous  facts  are  not  generally 
known,  hardly  ever  alluded  to  —  because  the  rule-of-three  intro- 
duced by  Kopp  still  remains  the  rule-of-thumb  in  the  German 
works  on  physical  chemistry,  and  a  few  men  in  high  official 
position  so  control  scientific  opinion  that  the  rank  and  file  do  not 
deem  it  necessary  to  study  such  publications  as  mine  in  the 
Comptes  Rendus  of  the  Academy  of  Sciences  of  Paris,  even 
though  they  were  presented  by  one  of  the  foremost  scientists  of 
the  nineteenth  century,  by  Monsieur  Berthelot. 

I  may  be  permitted  to  quote  a  few  prophetic  (and  approving) 
words  from  a  letter  of  Berthelot  of  October  9,  1891:  "I  must 
"  compliment  you  on  your  new  results  and  on  the  methodical 
"  sequence  and  the  elegance  of  your  deductions:  I  can  have  no 
11  doubt  they  will  make  an  impression  unless  statical  atomism 
"throws  a  veil  over  the  minds"  (of  the  chemists).  Our  work 
was  dynamic  (rotation,  moment  of  inertia)  ;  the  prominent  pro- 
fessors of  chemistry  are  hardly  even  in  statical  chemistry,  but  in 
rather  a  sort  of  statical  atomism  represented  in  structural  for- 
mula without  regard  to  really  statical  forces.  Instance  the  tetra- 
hedron of  so-called  stereo-chemistry.  See  General  Chemistry, 
1897,  p.  335. 

As  we  cannot  here  enter  upon  the  analytical  treatment  of  the 
subject  of  the  rotation  of  the  molecules  (which  would  require  a 
book,  the  introduction  to  which  are  the  140  pages  quarto  pub- 
lished as  Notes  in  the  Comptes  Rendus,  thanks  to  the  scientific 
spirit  and  independence  of  Berthelot},  we  must  close  this  subject 
with  the  following  statement  that  probably  will  be  understood  by 
all:*. 

The  moment  of  inertia  of  any  system  of  atoms  depends  more  on 


77 

the  relative  position  than  on  the  weight  of  the  atoms;  for  the  influ- 
ence of  each  weight  is  multiplied  by  the  square  of  its  distance  from 
the  axis  of  rotation . 

I  may  add  that  the  "  Anomaly  "  in  question  furnishes,  when 
examined  in  detail  by  my  calculation  of  the  moments  of  inertia, 
a  most  absolute  demonstration  of  the  result  above  arrived  at, 
namely,  that  the  atometer  of  the  triad  S,  Se,  Te  is  the  same  and 
about  double  that  of  oxygen. 

Thus  gradually  the  relative  dimensions  of  the  atoms  are  de- 
termined, not  only  by  one  method  of  procedure  but  by  concord- 
ant results  obtained  on  different  lines  marked  by  the  different 
fundamental  properties  of  the  chemical  elements. 

In  conclusion  I  beg  permission  to  refer  to  another  striking 
anomaly,  the  variation  of  the  fusing  point  of  aliphatic  compounds 
with  the  number  of  carbon  as  odd  and  even  in  the  same.  This 
anomaly  is  stated  in  larger  text-books  also  in  Traube's  recent 
book  (1904,  p.  203)  for  Baeyer  detected  this  anomaly  first  and 
he  must  be  mentioned.  This  anomaly  was  fully  accounted  for  in 
my  Note  X  (1891.  July  8)  and  used  to  determine  the  linkage  of 
the  carbon  atoms,  Note  XI  (1891,  Aug.  17).  Why  does  not  Dr. 
Traube,  whose  mind  is  not  entirely  controlled  by  that  of  Ostwald, 
study  the  Comptes  Rendus  on  the  subject  of  this  "  interessante 

Schmelzpunktsunregelmaessigkei  t," 
if  I  may  be  permitted  to  use  his  own  impressive  terms. 

THE    FORM    OF    THE    ATOMS. 

We  have  now  obtained  a  fair  knowledge  of  the  general  form  of 
the  atoms  of  the  chemical  elements.  Starting  with  the  monad  of 
definite  electrical  character  and  valence,  the  elements  of  each 
genus  result  in  the  manner  stated,  first  by  axial  addition  of  16, 
next  by  the  lateral  regular  addition  of  3,  3  and  6  times  this 
amount.* 


*  The  nullovalent  elements  seem  to  possess  a  different  structure,  if 
their  atomic  weights  commonly  accepted  are  reliable.  They  seem  to 
prove  a  quadratic  structure  and  a  corresponding  increase  on  the  sides 
thereof,  followed  by  increase  in  depth  or  thickness  according  to  the 
ratio:  1:  5:  10:  20:  30,  where  the  unit  He  is  4.  This  would  account  for 
most  of  their  distinguishing  properties. 


78 

We  have  not  yet  treated  of  the  form  of  the  element  atoms  of 
the  first  order,  the  monads,  beyond  the  incidental  demonstrations 
that  they  must  consist  of  as  many  bars  as  the  number  of  their 
valence.  We  ought  yet  to  obtain  some  definite  idea  as  to  the 
reason  of  that  wonderful  contrast  of  the  monads,  from  oxygen 
and  nitrogen,  through  carbon  and  boron  to  beryllium  and  lithium, 
which  we  have  termed  the  most  extreme  discontinuity  in  nature. 

In  order  to  do  so  we  must  recall  the  general  mode  of  enchain- 
ment of  the  atoms  in  chemical  compounds,  first  shown  in  our 
Programme  of  1867  (p.  12-13  for  the  typical  compounds)  and 
fully  demonstrated  in  our  Note  XI,  1891. 

Accordingly,  serial  organic  compounds  are  typically  repre- 
sented by  the  upper  figure  of  Plate  14,  showing  first  the  horizon- 
tal projection  of  the  five  atoms  of  carbon,  and  below  the  entire 
axonometric  drawing  of  the  atom  of  pentan.  The  three  co-ordi- 
nate axes  are  shown,  so  that  the  co-ordinate  of  the  center  of  each 
one  of  the  constituent  carbon  and  hydrogen  atoms  may  be  read 
off. 

Such  axonometric  drawings  are  described  in  my  Principles, 
1874,  where  I  called  them  stenographic  formulae  (pp.  63-64, 
Plate  I,  Fig.  4),  as  well  as  in  the  Programme,  1867,  p.  14. 

The  general  forms  of  the  serial  compounds  like  pentan  is 
therefore  prismatic.  On  this  basis,  the  molecular  volume  of  or- 
ganic compounds  was  determined  in  our  Programme,  1867,  in 
our  Contributions,  1868,  No.  2,  in  our  Principles,  1874,  p.  115- 
117,  and  in  our  Note  X,  1891. 

In  the  lower  half  of  Plate  14  we  have  given  our  horizontal  pro- 
jection of  an  atom  of  benzol ;  the  axes  X  and  Y  are  shown,  Z  is 
vertical  in 'the  center  or  origin  O. 

The  back  of  the  carbon  atoms  are  shaded  by  lines,  the  face  is 
left  open.  The  significance  hereof  is  best  shown  in  the  upper 
figure,  and  must  be  borne  in  mind  for  properly  understanding  the 
position  in  space  of  the  six  carbon  atoms  of  benzol. 

By  the  way,  the  latest  work  on  Stereochemistry  by  A.  Werner 
(Jena,  1894),  does  not  refer  to  me,  while  C.  A.  Bischojf  (Frank- 
furt, a.  M.,  1894)  refers  to  me  in  a  foot  note  (p.  15),  quoting 
from  Lotliar  Meyer's  famous  review  *  of  my  Programme  (see 


*  Zeitschr.  f.  Chemie,  N.  F.,  Bd.  6,  p.  446. 


79 

True  Atomic  Weights,  1894,  pp.  239-255),  in  a  most  demon- 
strative manner,  showing  how  thoroughly  Lothar  did  his  work.* 

It  is  truly  marvelous  how  the  modern  chemical  world  has  been 
misled  by  a  few  German  chemists  into  the  absurd  tetrahedral 
stereochemistry  which  itself  has  been  publicly  disavowed  by  its 
originator  van't  Hoff  of  the  University  of  Berlin  as  "  childish  " 
in  his  addressf  at  theDalton  Celebration  in  Manchester,  May  20, 
1903  —  twelve  years  after  I  had  proved  its  mechanical  absurdity 
in  the  Comptes  Rendus  (Note  XI,  Aug.  17,  1891). 

It  might  well  be  asked  how  it  is  possible  that  Professor  Werner 
in  1904  can  issue  a  "  Lehrbuch  "  of  500  closely  printed  pages 
octavo,  based  upon  a  principle  proclaimed  early  in  1903  by  its 
own  author  to  be  "  childish  ' '  and  which  had  been  proved  absurd 
by  me  in  the  transactions  of  the  Academy  of  Sciences  of  Paris  in 
1891. 1 

After  all,  I  am  inclined  to  cordially  thank  Professor  Werner  for 
having  omitted  my  name  from  this  book  of  his,  but  I  beg  to  be 
permitted  to  express  my  regret  that  such  books  are  in  fact  the 
sources  which  the  multitude  of  young  chemists  are  advised  to 
study  to-day. 

But  with  van  't  Hoff  and  Ostwald  at  the  head  of  a  great  organ, 
their  ' '  Zeitschrif t  f iir  physikalische  Chemie  ' '  anything  seems 
possible.  The  dreadful  effect  on  the  progress  of  science  of  such 
an  influence  of  a  few  scientific  men,  having  control  of  public 
scientific  opinion,  has  by  no  one  been  more  thoroughly  exposed 
than  by  Ostwald  himself  on  pp.  879  and  880  of  his  Electro- 
chemie,  Leipzig,  1896. § 

Ostwald  says  that  "  the  weight  of  this  opinion  depressed  the 
regard  for  those  contributions  to  such  an  extent,  that  even  those 


*  Meyer  "  hebt  als  verdaechtig  hervor  "  *  *  *  dass  Hinrichs  *  *  * 
"  operirt  mit  dualistischen  Formeln  "  *  *  *  "  alle  BetrachtuDgen  auf 
die  als  irrig  erkannte  (sic!)  Proust  'sche  Regel  basirt."  *  *  * 

t  Science,  V.  17,  p.  955;  1903,  from  Nature. 

t  The  collection  of  experimental  data  in  Werner's  book  is  most  valua- 
ble and  ought  to  show  him  that  they  are  in  full  accord  with  the  chemical 
structure  as  represented  in  our  work. 

§  I  just  see  a  report  on  the  Radium  lecture  by  Ostwald  before  the 
Chemical  Society  in  the  Koyal  Institution  at  London;  how  Faraday 
would  have  spoken,  if  he  had  been  present! 


80 

scientists  not  immediately  concerned  were  deterred  from  giving 
personal  examination  to  the  contributions  which  had  been  dis- 
carded with  such  energy.* 

Probably  this  accounts  for  the  fact  that  a  younger  American 
chemist  of  prominence,  a  professor  in  one  of  our  largest  Eastern 
Universities,  and  the  editor  of  a  chemical  journal,  in  a  friendly 
chat  of  chemists  during  the  last  meeting  of  the  American  Asso- 
ciation, at  St.  Louis,  about  New  Year,  1904,  declared  with  some 
show  of  pride  and  satisfaction :  li  I  know  nothing  about  the  form 
of  atoms." 

If  this  bright  disciple  of  Ostwald  had  not  been  blindedf  by 
the  crude  and  forceful  teaching  he  received  at  Leipzig,  he  would 
no  doubt  have  looked  into  the  Comptes  Rendus  with  open  eyes 
and  without  prejudice  —  and  I  am  sure,  he  would  have  easily 
understood  the  fundamental  points  about  the  form  of  the  atoms 
of  organic  compounds. 

Having  now  possibly  pushed  away  some  cobwebs  that,  as 
Ostwald  declares  emphatically,  some  time  are  spread  by  men  in 
high  scientific  positions  like  his,  to  the  great  loss  of  science  and 
to  the  lasting  injury  of  the  rising  generation  of  scientists,  we 
may  expect  that  the  unbiased  reader  has  acquired  an  idea  of  two 
forms  of  compound  atoms,  the  prismatic  and  the  tabular  or 
discoid. 


*  It  is  extremely  difficult  to  translate  so  loosely  verbose  a  philosopher 
(Naturphilosoph)  as  Ostwald;  I  therefore  transcribe  his  original  German 
from  which  we  have  taken  the  main  parts. 

Dieser  Umstand  drangt  zu  der  andern  moglichen  Auffassung  hin,  dass 
es  in  der  Thatder  Einfluss  einiger  im  Besitz  der  damaligen  offentlichen 
Meinung  beflndlichen  Physiker  war,  die  sich  MAGNUS,  dem  ausgespro- 
chensten  Gegner  HITTORF'S,  anschlossen,  und  durch  das  Gewicht  ihrer 
Meinung  den  Credit  jener  Arbeiten  in  solchem  Maasse  verminderten, 
dass  auch  die  nicht  unrnittelbar  Betheiligten  sich  einer  genauen  Prii- 
fung  dieser  mit  solcher  Energie  abgelehnten  Arbeiten  uberhoben 
glaubten. 

t  Ostwald,  same  page  already  quoted  from,  says :  — 

Kamn  man  sich  denken,  dass  zu  jener  Zeit  sammtliche  Geister  so  mit 
Blindheit  geschlagen  waren,  dass  sie  diese  einfachen  Dinge  nicht  sehen 
konnten? 

Indeed,  we  need  not  imagine  such  a  sad  condition,  but  have  seen  it 
exemplified  for  a  dozen  years  by  the  organ  of  Vatft  Hoff  and  Ostwald. 


81 

These  forms  are  exemplified,  the  first  by  the  aliphatic  (or 
alcoholic)  organic  compounds,  the  latter  by  the  aromatic  com- 
pounds. 

Next,  we  must  ask  the  reader  to  remember  that  we,  by  strict 
mathematical  deductions,  have  determined  from  these  forms  the 
fusing  and  boiling  points  of  enough  series  of  organic  compounds 
to  prove  the  reality  of  these  forms  by  the  concordance  of  the 
calculated  and  observed  boiling  and  fusing  points. 

We  may  therefore  properly  call  these  terms  of  the  compound 
atoms  —  prismatic  and  tabular  —  demonstrated  by  the  ther- 
mometer's indication  of  boiling  and  fusing  points,  exactly  as  the 
form  of  the  earth  has  been  demonstrated  by  a  corresponding  train 
of  exact  mathematical  deductions  together  with  the  observed 
oscillations  of  the  pendulum  at  distant  points  on  our  globe. 
These  two  cases  of  investigation  are  exactly  parallel ;  and  from 
all  we  know  by  their  writings,  both  Ostwald  and  van't  Hoff  would 
have  ignored  or  ridiculed  the  mathematicians  and  astronomers 
who  determined  the  form  of  the  earth  by  the  pendulum,  as  they 
have  ignored  or  ridiculed  my  work  of  determining  the  form  of  the 
atoms,  for  they  are  unable  to  comprehend  the  mechanical  steps 
involved  in  both  of  these  important  researches. 

Now,  it  has  long  been  demonstrated  by  mathematicians  in  that 
great  branch  of  this  fundamental  science  called  analytical 
mechanics,  that  the  two  principal  permanent  axes  of  rotation  for 
any  body  or  any  system  of  rigidly  connected  bodies  (say  the 
atoms  of  a  chemical  compound)  are  determined  by  the  weight 
and  position  of  the  parts  or  particles  of  the  body  or  system. 

For  a  sphere,  the  maximal  and  minimal  moment  of  inertia 
coincide,  their  ratio  is  one,  and  really  any  diameter  of  a  sphere  is 
a  permanent  natural  axis  of  rotation. 

For  a  circular  disk  the  axis  at  right  angles  to  the  disk  at  its 
center  has  the  maximal  moment  of  inertia,  exactly  double  the 
minimal  moment  for  any  one  of  the  diameters  of  the  disk. 

For  a  prismatic  body  —  a  rod,  or  a  bar  —  the  minimal  axis 
coincides  with  the  geometrical  axis,  while  the  maximal  axis  is  at 
right  angles  to  the  bar  at  the  center  of  the  same  ;  and  further  the 
ratio  obtained  by  dividing  the  maximal  moment  by  the  minimal 
moment  increases  indefinitely  with  the  length  of  the  prism. 

6 


82 

Now,  since  we  have  demonstrated  in  the  publications  specified, 
which  have  been  issued  during  the  last  forty  years,  that  the  fusing 
point  is  determined  by  the  minimal  moment,  and  the  boiling  point 
by  the  maximal  moment  it  follows,  that 

for  alcoholic  or  aliphatic  compounds,  the  atomic  form  being 
prismatic,  the  fusing  and  boiling  point  curves  must  greatly 
diverge  with  increasing  atomic  weight ;  while 

for  aromatic  compounds,  the  atomic  form  being  tabular,  the 
fusing  and  boiling  curves  must  run  mainly  parallel  to  one  another. 

Plate  15  represents  the  observed  fusing  points  (black  circles) 
and  boiling  points  (open  circles)  of  the  hydrocarbons  as  ordi- 
nates  to  their  atomic  weight  as  abscissae. 

We  see  that  the  curves  for  the  prismatic  paraffins  diverge , 
while  the  curves  starting  from  Benzol  respresenting  the  aromatic 
hydrocarbons  run  mainly  in  parallel  direction . 

This  great  general  fact  has  never  been  accounted  for  —  and 
indeed,  has  practically  been  overlooked;  but  it  is  very  real,  and 
though  its  strictly  mathematical  demonstration  may  not  be 
comprehended  by  all,  it  will  be  admitted  by  all  who  have  the 
necessary  mathematical  training. 

Before  we  make  any  application  of  this  fundamental  relation  to 
the  chemical  elements,  it  may  be  advisable  to  show  one  of  the 
striking  applications  hereof  to  certain  dominant  but  scientifically 
unproved  chemical  opinions.  It  is  universally  believed  by 
modern  chemists,  that  the  substituted  atoms  in  the  so-called  para 
compounds  are  opposite,  while  in  the  ortho  position  they  are 
neighboring  places  in  the  benzol  atom  or  as  it  is  commonly  called, 
the  benzol  ring. 

It  is  greatly  to  be  regretted,  that  the  designations  ortho  and 
para  based  on  actual  derivation,  have  practically  disappeared  from 
the  pages  of  our  chemical  literature  and  have  been  replaced  by 
the  numerals  1,  2  and  1,  4  expressing  the  supposed  places  above 
given. 

Now,  in  my  numerous  and  very  laborious  calculations  of  the 
moments  of  inertia,  1  have  also  calculated  the  two  moments  for 
substitutions  in  the  benzol  atom  (Plate  14)  in  neighboring 
(actual  places  1,2)  and  in  opposite  (actual  places  1,  4)  places. 


83 

The  result  was  that  the  ratio  of  the  two  moments  is  greater  for 
the  opposite  than  for  the  neighboring  substitution. 

That  means,  the  fusing  points  must  be  lower  for  opposite 
substitution,  higher  for  neighboring  substitution,  since  the 
maximal  moments  do  not  vary  much. 

Plotting  the  actually  observed  boiling -fusing  points  of  the  para 
and  ortho  compounds,  as  shown  by  Plate  16,  we  find  indeed  the 
corresponding  boiling  points  practically  the  same,  but  we  see 
that  the  fusing  points  of  the  ortho  compounds  are  throughout 
much  lower  than  the  para  compounds. 

According  to  our  so  generally  confirmed  mathematical  princi- 
ples we  must  therefore  conclude,  that 

the  para  compounds  are  neighboring 
or  1,  2  substitutions,  and 

the  ortho  compounds  are  opposite 
or  1,  4  substitutions. 

This  crucial  test  therefore  proves  that  the  opinion  universally 
taught  by  all  modern  structural  chemists  cannot  be  true,  unless 
it  be  shown  that  the  entire  system  of  our  atom-mechanics  is  false. 

As  a  preliminary  step  to  obtain  such  a  demonstration  it  will  be 
necessary  for  our  modern  structural  chemists  first  to  study  this 
our  system  of  atom-mechanics. 

It  may  be  a  little  hard  to  begin  this  not  easy  study ;  I  can 
assure  the  structural  chemist  that  it  will  take  solid  mathematical 
training  and  not  mere  fct  childish  play  with  tetrahedrae." 

If  that  study  is  undertaken,  I  venture  to  say,  that  there  will 
be  a  total  change  of  heart,  that  the  scales  will  fall  from  the  eyes 
of  our  modern  chemists. 

But  it  is  unbecoming  for  me  to  picture  the  result,-  1  will  let 
Ostwald  express  it :  — 

"  Zwar  spat,  aber  dann  um  so  nachdriicklicher  hat  sich  die 
"  Anerkennung  dieser  klassischen  Arbeiten  Bahn  gebrochen, 
"  und  zwar  durch  den  Um  stand,  dass  auf  andern  Boden  That- 
44  sachen  entdeckt  warden,  welche  zu  der  gleichen  Auffassung 
"  drangten."  1.  c.  pp.  879-880. 


84 

Of  course,  Ostwald  is  always  extravagant  in  his  statements, 
and  therefore  too  complimentary ;  we  will  not  say  that  our  work 
is  classical.  But  we  dare  say,  that  we  have  retraced  every  step 
carefully,  these  many  years,  and  we  have  taken  every  possible 
care  to  avoid  errors. 

For  that  reason  we  feel  confident  that  the  statements  made  by 
us,  in  all  essential  particulars,  will  be  confirmed  by  every  con- 
scientious and  really  competent  investigator  who  shall  now  or  at 
any  future  time  repeat  our  calculations. 

And  since  now  ' '  on  another  ground  facts  have  been  discovered 
which  lead  to  the  same  conclusion  "  (to  -repeat  part  of  the  last 
words  of  Ostwald)  we  may  really  expect  that  our  work  will  re- 
ceive general  attention,  since  to-day  chemists  appear  no  longer  to 
shy  at  our  first  statement  that  the  chemical  elements  really  are 
compound  bodies. 

We  admit,  that  the  "Radium-Craze,"  as  Winkler  so  appro- 
priately has  called  it,  takes  quite  too  easily  to  the  notion,  that 
some  of  our  elements  have  been  decomposed  already  ;  but  if  our 
modern  chemists  are  bound  to  be  led  astray,  may  they  not  for 
once  through  error  get  into  the  right  way  ? 

Since  they  now  without  an  effort  begin  to  think  of  the  elements 
as  compounds,  we  may  hope,  that  the  younger  generation  will 
undertake  the  study  from  which  for  forty  years  chemists  have 
been  deterred  by  this  false  notion  that  our  very  starting-point  was 
wrong. 

Hoping  that  the  reader  now  has  acquired  a  reasonable  concep- 
tion of  the  form  of  the  atoms  of  compound  bodies,'  we  may  turn 
back  to  the  form  of  the  simplest  of  all  chemical  elements,  the 
monads  or  elements  of  the  first  order  consisting  of  but  one  single 
group  of  pan-atoms. 

Not  able  to  present  our  full  work  on  atomic  forms  in  this 
popular  outline,  we  must  here  confine  ourselves  to  a  statement  of 
final  results  deduced,  followed  by  some  explanatory  remarks. 

We  therefore  state,  as  the  final  result  of  our  investigations, 
that  the  general  form  of  the  monad  atom  is  prismatic  for  the  true 
metalloids,  which  are  pronouncedly  electronegative,  and  that  it  is 
tabular  for  the  true  metallic  monads  and  for  boron  and  carbon. 

In   other  words,  the  metalloids  correspond  to  aliphatic  com- 


85 

pounds,  while  the  metals  correspond  to  aromatic  compounds. 
Or,  again,  the  prismatic  element  atoms  are  electro-negative,  the 
tabular  atoms  are  electro-positive. 

The  four  double  disks  of  a  carbon  atom  may  group  molecularly 
in  three  forms  at  least,  which  may  correspond  to  only  single,  or 
including  double  and  treble  atomic  ties ;  the  second  probably  is 
graphite,  the  last  is  the  diamond.  Such  a  body  will  show  an 
enormous  cohesion  and  relatively  high  density  or  very  small  atomic 
volume.  This  implies  highest  fusing  and  melting  point. 

From  this  central  form,  we  have  tabular  forms  towards  the 
metals,  prismatic  towards  the  metalloids. 

As  the  valence  becomes  less,  that  cohesion  will  be  lessened,  a 
less  number  of  parallel  forms  being  present.  Hence  fusing  and 
boiling  points  will  be  lowered  ;  from  general  mechanical  principles 
we  conclude  the  temperature  change  to  vary  in  a  geometrical  ratio 
while  the  number  of  components  (i.  e.  the  valence)  varies  in  an 
arithmetical  ratio.  The  valence  represents  approximately  the 
logarithm  of  the  temperature  change. 

The  effect  of  the  axial  and  lateral  increase  of  the  monad  by  the 
sixteen-group  in  the  manner  so  often  specified,  will  gradually 
make  these  common  masses  added  dominant  and  thus  make  the 
higher  members  of  the  genera  more  nearly  alike  in  their  physical 
properties. 

THE  ATOMIC  WEIGHT  OF  PANTOGEN. 

It  now  remains  to  determine  the  atomic  weight  of  primitive 
matter,  the  pantogen. 

Since  hydrogen  has  the  lowest  atomic  weight  of  all  elements 
and  is  taken  as  one,  it  follows  that  the  atomic  weight  of  panto- 
gen  depends  on  the  number  of  pantogen  atoms  combined  to  form 
one  atom  of  hydrogen. 

We  have  from  the  first,  been  convinced  that  the  number  is 
two ;  all  our  extended  examinations  have  confirmed  this  result. 

Therefore  the  atomic  weight  of  pantogen  is  one  half  that  of 
hydrogen  or  one  thirty-second  that  of  oxygen. 

The  atomic  number  of  any  element  is  the  number  of  pantogen 
atoms  forming  one  atom  of  that  element. 


86 

Hence  the  atomic  number  of  hydrogen  is  2,  of  oxygen  32, 
sulphur  64,  silver  216,  lead  414. 

The  laws  of  symmetry  make  the  even  atomic  numbers  much 
more  probable  than  the  odd  atomic  numbers.  This  is  confirmed 
by  the  fact  that  we  find  really  only  two  elements,  namely,  chlo- 
rine 71  and  copper  127,  for  which  the  odd  number  may  be 
considered  established. 

All  other  elements  having  an  even  atomic  number,  therefore, 
must  have  a  whole  number  for  atomic  weight  if  the  atomic  weight 
of  hydrogen  be  taken  as  one. 

Now,  this  statement  is  denied  by  a  majority  of  the  chemical 
world,  especially  by  the  official  part  thereof,  which  has  combined 
in  the  issue  or  annual  proclamation  of  atomic  weights,  called 
international  atomic  weights. 

The  question  at  issue  is  not  the  amount  of  difference,  the 
insignificance  of  the  numerical  value  of  the  fractions,  but  the 
very  existence  thereof.  It  is  a  question  of  principle  of  highest 
i  rnportance ;  for  on  the  final  decision  thereof  depends  the  recog- 
nition of  the  unity  of  matter. 

We  have  fully  examined  this  question  in  the  fourth  series  of 
our  Notes  (Nos.  XXV  to  XXXIII)  and  especially  in  our  two 
works : 

The  True  Atomic  Weights,  1896,  and 

The  Absolute  Atomic  Weights,  1901. 

It  is  impossible  to  briefly  consider  the  main  points  in  a  popu- 
lar form  in  this  place ;  the  present  book  has  already  passed  by 
far  the  limits  originally  set  for  the  same. 

We  therefore  must  refer  those  of  our  readers  who  desire  to 
examine  into  this  great  question  to  the  above  works  of  ours, 
especially  the  last  named  one. 


CONTENTS. 

Halftone-Portraits  with  Autographs  of   Seven  Eminent  Scientists  who 
have,  assisted  the  author. 

List  of  Publications  on  Atom-Mechanics    .  .  VII 


Characteristic  Properties,  Genera .     page     1 

Boiling-Fusing  points       "... 9 

Atomic  Weights  of  the  Elements  .     .     .     .     ,     . 11 

Fusing  Points  and  Atomic  Weights .    .     .    .     .  14 

Fusing  Points  and  Valence* .     .    .    ,     .     .  24 

The  System  of  Atomic  Weights  f 42 

Total  Number  of  Elements  and  the  Cosmochemical  System      ...  47 

Frequency  and  Distribution  of  the  Elements 50 

The  Atomic  Volume  of  the  Elements  J    .     .    ..    «    .     »    .     .    .     .     .  52 

Radio-active  Elements     .     .     ....     .     .     .     . 63 

The  Decomposition  of  the  Elements       . 66 

So-called  Anomalies  due  to  Form  of  the  Atoms    .,.     .     ,    .     .    .     .  71 

Fusing  Point  Anomaly      .     .     ......     ,     «     ...    ...  72 

Boiling  Point  Anomaly§  .     .     ....     .     .     .    .     .     .     .     .     «     -    .     .  75 

The  Form  of  the  Atoms    .     . 77 

The  Atomic  Weight  of  Pantogeu •.     ,     .     .     ...     .  85 


Sixteen  full  page  Plates .      Plate  1  to  16 


*  First  inductive  Determination  of  the  structure  and  form  of  the  Element 
Atoms. 

t  Confirmation  of  the  same. 

J  Second  Confirmation  of  same. 

§  Third  Confirmation  and  Determination  of  the  length  of  the  atoms  of  the 
Sulphoids. 

(87) 


PLATE  I. 


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PLATE  2. 


SQO° 

Fusing  Points 

Absolute  Zero  ,  -273'C, 


PLATE  3. 


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THE 

ABSOLUTE  ATOMIC  WEIGHTS 

OF  THE 

CHEMICAL  ELEMENTS 

ESTABLISHED   UPON  THE   ANALYSES 
....  OF  THE  .... 

CHEMISTS  OF  THE  NINETEENTH  CENTURY 

AND   DEMONSTRATING  THE 

UNITY  OF  MATTER; 


PRESENTED  IN   SIMPLE   LANGUAGE 
.  .  TO  THE  .  . 


GENERAL  SCIENTIFIC  PUBLIC, 


GUSTAVUS  DETLEF  HINRICHS,  M.  D.,  LL.D., 

Honorary  and  Corresponding  Member  of  Scientific  Societies  in 

Austria,  England,  France,  Germany  and  the  United  States; 
Professor  of  Chemistry  in  the  St.  Louis  College  of  Pharmacy. 


WITH  A  PORTRAIT  OF  BERZELIUS  AND  THREE  PLATES, 


ST.  Louis,  Mo.,  U.  S. 

CARL  GUSTAV  HINRICHS,  PUBLISHER. 
1901. 

This  book  (pp.  xvi,  304,  8vo,  paper  cover)  may  be 
obtained  from  any  bookseller.  It  will  also  be  mailed,  post- 
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